How important was the Act of Union (1707) to the growth of the already existing English empire? Would England itself have had a comparable empire in size to the British Empire had it not formed the Kingdom of Great Britain with Scotland?

The problem with these questions is that its hard to state 'how important' something is in any definitive numerical or quantative sense and it borders on alternative history speculation. Also many of these questions act as if Ireland and Wales, and their economic and human resources didnt exist. Britain, Wales, Ireland and Scotland already had a common common ruler. So even though the Scots Parliament were seperate it doesnt mean that if they had stayed seperate they would have run entirely independently from the UK. Its entirely plausible that they would have run things as joint ventures, or Scottish soldiery employed/hired by the UK, an independant Scotland could well have supplied units to the British during the Napoleonic wars etc.

But assuming that Scotland did a sort of Switzerland I still doubt much would have changed overall, they only represent about 10% of the UKs manpower, and at the time perhaps less of the economy. This isnt to dismiss their immense cultural and intellectual contribution, just that it wouldnt have made a massive difference from an economic or manpower perspective. If the US colonies had 10% less people, if France had 10% less people, etc etc then how much of a difference would their arcs through history have been? Its very hard to gauge unless you can identify some special 'tipping point' that a lack of something might have altered. Often too in these speculative scenarios people propose changing one aspect of a situation, but dont anticipate that that change means that the people concerned would then have reacted differently to other things. That is, without Scotland the UK may have found other resources that we can't anticipate; for example they may have chosen to make peace with the American colonies, give them access to what they wanted, and forged a close bond resulting in an even larger more expansive Empire. But I think we're passing wayyyy out of History with that.