In a word, no... they would not be left alone by the law. Loving v. Virginia actually deals with a very similar situation to what you've described. Richard Loving, a white man, and Mildred Jeter, a part native and part black woman, did not marry nor attempt to marry in Virginia, where they both resided in the small farming community of Central Point within Caroline County. Their crime was being married while in Virginia, not marrying within Virginia itself.

They were both born in the 1930s, him in '33 and her in '39, and they grew up near one another, becoming acquainted when she was about 11 and he 17 through her older brother who often played music at his home that friends and neighbors frequently came by to enjoy. At some point the pair fell in love, and in Jan of 1957 they had a son... but marriage between whites and blacks (any person of color, actually) had been expressly prohibited (this time) by a 1924 law passed by the Virginia legislature. Their child had been delivered by the local midwife - non other than Loving's own mother, and the couple lived separately. Richard worked for a relative of Mildred - it was a small community where everyone knew everyone.

In May of '58 they traveled to D.C. to obtain a marriage license, and on June 2nd, 1958, Richard and Mildred vowed to love each other eternally, and officially, in what was effectively an elopement ceremony held in Washington, D.C. by a local preacher, Pastor John Henry. They were now legally married and so they headed back home. Their honeymoon bliss, however, would be shortlived. On July 14, 1958 an arrest warrant was issued for Richard (Mildred's is actually dated several days later) and in an early morning raid they were arrested by sheriff Garnett Brooks with the help of two of his deputies.

They knocked a couple times. I heard ’em, and before I could get up, you know, they just broke the door and came right on in. - Richard Loving

It was about 2 am, and I saw this light, you know, and I woke up. There was the policeman standing beside the bed. And he told us to get up, that we were under arrest. . . . They asked Richard who was that woman he was sleeping with, and I said, ‘I’m his wife,’ and the sheriff said, ‘Not here you’re not.’ - Mildred Loving

Loving would spend one night in the lockup but was not permitted to bail out his 18 year old wife, despite her being five months pregnant at that time. She remained locked up for nearly a month. In addition to being found in the same bed sleeping, the officers had also located the couple's wedding certificate during the raid, which was used as evidence they were married in violation of Virginia law. In January of 1959 the couple pleaded guilty to miscegenation, a felony per the 1924 bill, and were both sentenced to one year in jail. The judge offered a suspended sentence for both if they immediately left Caroline County and, indeed, the State of Virginia itself for a period of no less than 25 years. The couple was heartbroken to leave the town and neighbors they loved, their friends and their family. They moved to D.C. where Mildred had relatives and essentially began again, raising their three boys there, but always longing to return home. They didn't want to change any laws beyond how they applied specifically to them - in other words, they never set out to change the world.

I didn’t want to, you know, leave away from ’round my family and my friends... When I was in Washington, well, I just wanted to go back home.

My older son came back and told me that Donald [another son] had been hit by a car... I knew I had to go to him, but I didn’t know if he were dead... He was sitting up in the street crying. And I think that was the straw that broke the camel’s back. I had to get out of there. I wasn’t in anything concerned with civil rights. I was trying to get back to Virginia... I was so unhappy, I was complaining to my cousin constantly. So one Saturday, I guess she got tired of it, she told me, ‘Write to [Atty General] Bobby Kennedy. He’ll help you. That’s what he’s up there for.’

Mildred wanted to fight the ruling, so she took action and within one month the Attorney General of the United States, Robert F Kennedy, had replied, directing her to the ACLU. Soon, in November of 1963 and with the help of ACLU lawyers, a petition was filed that...... went nowhere but the judge's desk drawer. In July of the following year the Civil Rights Act was passed by congress. Their petition then went to the Virginia Supreme Court, wherein the decision was effectively confirmed. A judge, the one who had been sitting on the Nov '63 petition to vacate the sentence, ruled on the case at the direction of the three judge panel of the high court in Richmond;

Almighty God created the races white, black, yellow, malay and red, and he placed them on separate continents. And but for the interference with his arrangement there would be no cause for such marriages. The fact that he separated the races shows that he did not intend for the races to mix. - Judge Bazile ruling on the petition to vacate the sentence

They had lost, again, but had also dodged a bullet. Had their case been ruled oposite and the ruling vacated they could have immediately been resentenced under their guilty plea, facing up to five years imprisonment each. Unfettered by the setback their legal team - a 29 and a 30 year old that were both pretty fresh out of law school - filed a motion with the Supreme Court of the United States. In the summer of 1967 SCOTUS came to the unanimous decision that marriage was a fundamental Right of We the People and no laws could be established or enforced to prevent interracial marriages. Virginia had argued their case by insisting the law was fair - both races charged with the crime were sentenced equally, preventing any discrimination. Chief Justice Earl Warren disagreed, citing that there were no laws preventing two non-white races from marrying and therefore the law was, in fact, discriminatory, and, subsequently, all similar laws in any state violated the Due Process and Equal Protection clauses within the 14th Amendment.

16 different states would have their racially motivated laws struck down that day - Richard and Mildred Loving had changed the world, and they could return to their home at last.

On a related yet anecdotal note (sorry mods!), I can share a similar story from my family. My grandfather graduated high school in 1942, then immediately enlisted (along with all males in his senior class) in the US Navy at the recruiting office. He was assigned as a Pharmacist's Mate, 2nd Class, and sent to Boston. Due to family sickness he never deployed but remained in Boston, and it was there he met a first generation American girl, the daughter of Antonio Rubicco and Teresa Colantuono, both born and raised in Italy. Antonio had migrated in 1908, Teresa a couple years later, but they had married in Italy before Amtonio left. My grandfather fell in love with this girl, and at wars end he married her and brought her back to Tennessee with him. When their landlord found out an Italian was living in the apartment my grandfather had rented, regardless of the fact they had been married before leaving Massachusetts, the landlord evicted them on the spot. While it wasn't unlawful for them to live together or be married it was too far out of "accepted" norms for a great many folks in society at large, and they would take action as they saw fit. A horrendous series of lynching and race riots from the 1890s to the 1960s proved this a thousand times over.