Frankly no. There is no credible evidence that FDR or those in charge of the Navy intentionally allowed the attack to occur.

While FDR did take a firm stance with Japan, and most in the Navy and Washington assumed war was inevitable to a degree, that is a long way from knowing the enemy was planning an attack and allowing it to occur.

Navy Cryptology (code breaking) was not able to read the IJN's primary codes in the lead up to war, and it would take well into 1942 for meaningful decrypts to happen, mostly because more messages means it is easier to spot patterns and make breaks. So you combine the inexact signals intelligence, and the fact that the Kido Butai was radio silent as soon as they left Japan, means that there was no real way that their location, or intentions could have been discerned. Then factor in that there route took them through the e=staggeringly empty North Pacific(a region as large as the US, and without any shipping lanes or islands to base patrol craft out of).

And from a logical perspective it doesn't hold up either. The US very much would have fought over the Philippines, with a war starting there likely escalating in size and scope, with strikes on Hawaii, Guam, Wake, Midway or California possible to cement US commitment. But to start the actual fighting the Japanese didnt need to risk everything with a trip all the way across the Pacific.

And if the attack was allowed to occur it puts the US on about as bad a footing as could be conceived to start the war. Battleships were still planned to be of great import, so why would you allow most of them to be sunk? Why would you allow your service branch(the Navy) which would have to do the lion's share of the work, get a sucker punch and suffer terrible morale and defeatism. Seriously the morale in Hawaii and he fleet until the Spring of 1942 was near rock bottom, particularity after an attempt to rescue Wake Island was called back last minute.

So the only way it makes sense to allow it to occur is if you want to handicap yourself to the greatest possible degree. FDR was not that foolhardy, having served as SECNAV, and being one of the most knowledgeable on naval matters of all the Presidents.