No. That's not possible. You can only update one table at a time unless that table has triggers which update other tables.
I suspect you just need to do this...
Update T1 set col2 = 'X' from T1 join T2 on T1.col1 = T2.col1
Update T2 set col2 = 'Y' from T1 join T2 on T1.col1 = T2.col1
Ryan Randall
Solutions are easy. Understanding the problem, now, that's the hard part.