Assuming that each partial band and stack obeys the basic rules of sudoku, your conjecture follows from the facts that

- Completed B1,B2,B6,B9 => at most one choice for B3
- Completed B4,B6,B2,B8 => at most one choice for B5
- Completed B8,B9,B1,B4 => at most one choice for B7

I'll grind through the first of those in what follows.

Row 1 has six values filled in, leaving three to go in r1c7-9 in some order: call these three choices n1,n2,n3. Same goes for row 2, with choices n4,n5,n6 say; and row 3 with choices n7,n8,n9. Since the total collection of filled-in numbers (B1,B2) plus choices (for B3) contains three copies of each digit 1-9 (one copy per row), and the (B1,B2) part accounts for two of those copies (one in B1, the other in B2), it must be the case that {n*} are the digits 1-9 in some order.

So, whatever digit d you think of, you know what minirow in B3 it must appear in. By similar reasoning, you know what minicol it must appear in. In other words, each digit 1-9 has only one allowed position in B3. If these nine positions are all distinct, you have one solution for B3; if not, you have no solutions.