If you use a double-pole GFCI breaker designed for this purpose, you'll be fine. The CT will simply enclose both hots and the neutral at the same time, and will still balance the net current, which will be 0 regardless of unbalanced current on the neutral unless there is actual leakage to ground.
You could potentially also install two GFCI receptacles and feed them both with a single neutral, but you would have to split the neutrals on the load side of the GFCI receptacles and keep them segregated from that point on.
What you can't do (and hopefully wouldn't try!) is to share the protected neutral of the GFCI circuit with another circuit like in techie's kitchen.
