Yes, they are the same. As you can see from the disassembly, 'a' and 'b' live in sequential memory locations:
Unit26.pas.32: a := a + 'a';
004552C8 B814874500 mov eax,$00458714
004552CD BAF0524500 mov edx,$004552f0
004552D2 E809F8FAFF call @LStrCat
Unit26.pas.33: b := b + 'b';
004552D7 B818874500 mov eax,$00458718
004552DC BAFC524500 mov edx,$004552fc
004552E1 E8FAF7FAFF call @LStrCat
In my case, @a = $00458714, @b = $00458718.
Note, however, that you have to enable Assignable typed constants setting to compile such code.
If you don't have this setting enabled, you have to move 'b' out of the procedure. The following code will not compile.
var
a: string = 'aaa';
procedure SubMethod;
var
b: string = 'bbb'; // <-- compilation stops here
begin
a := a + 'a';
b := b + 'b';
end;