No. Batteries supply potential difference.
The positive terminal of A(I'll call it A+) is at a higher potential than the negative terminal of A(A-). The same goes for B. However, we don't know if A- and B+ are at the same potential, so we can't conclude that A+ is at a higher potential than B-.
In fact, A+ and B- are at the same potential, as it is the lowest energy configuration of this system.
For a capacitor to work, there needs to be a potential difference across its ends. Here, there isn't.
Besides, a battery only works when charge is being drawn/added from/to both terminals. Electrostatic repulsion will not let the battery supply charge from just one terminal. Don't look at a battery as a producer of charge. Look at it as a separator of charge. For every positive charge A shoots out of its positive terminal, there will be a negative charge that gets stuck on its negative terminal; which will work to prevent more negative charges from accumulating on A-. If negative charge can't accumulate on A-, then A+ will stop shooting out charges. This happens very quickly -- you won't be able to measure the amount of charge that A+ released.
However, if you connect A- and B+, then A- and B+ will be at the same potential, and A+ will be at a higher potential that B-, and the capacitor will charge.