It's fine to note that this recorded Alexander Brown may be yours, and to look for additional evidence, but without that additional evidence it's only a working hypothesis.
Following on from this, Alexander Brown married around 1815 Isabella Reid. Now the 1851 census states Isabella Reid was born in Strichen, Aberdeenshire, and from this census and her death puts her birth as c1782-1785.
Now the only baptism of someone with that name was an Isabel Reid in Strichen in 1782 to James Reid and Elizabeth Rennie. Now while I know Isabella could be a variant I was always a bit cautious of it so as you say it was a bit of of a hypothesis.
Well last month I was in Aberdeen and in the kirk sessions to see if I could find anything in Fraserburgh or Peterhead kirk sessions about their daughter Elizabeth Brown born c1818-1821 who had an illegitimate daughter Isabella born in 1840.
The baptism in Peterhead said Elizabeth was lately in Fraserburgh and in the latter kirk sessions I found the whole story of the illegitimate birth. It named the father as seaman Robert Allan but more interestingly to me stated that Elizabeth Brown had been living in Fraserburgh with Alexander Burnett and her aunt Elizabeth Reed.
Well this was all rather exciting as the Isabella Reid baptised in 1782 had a sister Elizabeth Reid baptised in 1783. And thanks to the census showing her age and birthplace and the fact Elizabeth Reid/Burnett died in 1855, I was able to prove that my ancestor Isabella's baptism was indeed that 1782 one. Working sideways and in other areas can be very useful.
However one question this has thrown up is who were the 15 and 13 year old William Read [sic] and Elizabeth Read [sic] with the Burnetts in the 1841 census. I suspect they were the children of elder brother James Reid (1780-1862) but the jury is still out on that one for now!