Burns uses the "for a' that" line ending on more than one occassion. Some seem to date "Is There For Honest Poverty" to 1795 which is the same year that he wrote the "Ballads On Mr Heron's Election 1795" This has seven verses whic all use the same device and fit the same tune etc. Verse one is

Whom will you send to London town
To parliament and a' that?
Or wha in a' the country round
The best deserves to fa' that?
For a' that an a' that
Thro Galloway an a' that
Where is the Laird or belted knight
The best deserves to fa' that

He didn't just use the device and verse type for political thought. A decade earlier he wrote the lyrics actually titled "For A' That" which starts off

Tho' women's minds like winter winds
May shift, and turn, an a' that
The noblest breast adores them a'
A consequence I draw that

For a' that an' a' that
And twice as meikle's a' that
The bonnie lass that I lo'e best
Shall be my ain for a' that

SO I think it is likely that his use of "an a' that" in the song in question is just him using a familiar device, verse structure and rhythm etc rather than reading anything else into it. There may well be other instances as I didn't look through the whole canon. He also often uses the device where he says "man" at the end of various lines. I'm not sure if he was the first to use these? He very possibly wasn't!