The short answer to this question is 'more or less yes'. That said, let me preface the long answer by stating that I am not an economic historian by specialization so in answering this question my focus will primarily be on the politics surrounding the Act of Union that had an impact upon the economy of Scotland at that time. Hopefully it will still give you a better understanding of the issue at hand.
In 1698 the Scottish attempted to break into global trade by establishing a colony on the Isthmus of Panama which was intended to control access between the Atlantic and Pacific Oceans. As the English held trade with the North American colonies in an iron grip, the Darien scheme represented to many Scots the only way Scotland would be able to compete with other trading European nations. Unfortunately, both settlement attempts failed, resulting in a loss of the total capital raised (around £400,000 or about one-fifth of Scotland's total wealth). As Scots of all walks of life had invested in the scheme, most of the population was affected to some extent, with members of the Lowland aristocracy sustaining some of the greatest losses of all. When attempts to recoup these losses failed (including a petition to William III for aid in reclaiming and settling the land in Panama which was rejected for fear that it would provoke war with Spain), the Scottish economy sank into further depression which was not aided by the parliamentary posturing that took the form of several acts passed in the first five years of the eighteenth century.
When Queen Anne succeeded her sister and brother-in-law, she did so childless, her son and heir, the duke of Gloucester having died at the age of 11 in 1700. In 1701 the English Parliament passed the Act of Settlement that devolved the English crown upon Sophia of Hanover, a granddaughter of James VI/I by his daughter, Elizabeth, Queen of Bohemia. As this act was passed without consultation with the Scottish Parliament, the Scots refused to recognize it and instead drew up the Act of Security (1704) which stipulated that following Anne's death without heirs, the Scottish crown would go to a Protestant candidate descended from Scottish kings...but not the one chosen by the English unless the English were willing to make certain economic, political, and religious concessions to the Scots. While Anne at first refused to give this piece of legislation the Royal Assent, her hand was forced when the Scots refused to raise taxes and threatened to recall their regiments serving under the duke of Marlborough on the Continent. In retaliation, the English Parliament then passed the Alien Act in 1705 which classed Scottish nationals in England as foreign aliens and any English property owned by Scots as the property of foreign aliens. This had the effect of making inheritance much less certain for these families and also refused them certain legal rights as well within England. It also put an embargo on the import of Scottish goods into England and the English colonies which practically nailed the lid on the coffin on any Scottish trade whatsoever. Yet the Alien Act contained a provision that outlined the act's suspension should the Scots enter into negotiation with the English about the union of the two parliaments.
So, with that context in mind, the provisions negotiated between the two nations at the time of the union in 1707 can be seen to have had a positive impact on Scotland's economy, however, one can also make a case for the Scots economy having been crippled in the first place by English protectionism. Still, to give you an idea of how the economy improved, here are some of the provisions accorded to the Scots by the Act of Union:
I'm sure someone who has a more detailed knowledge of historical economies would be able to expand upon my answer accordingly but hopefully this will at least give you an overview on the topic.
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