I'm installing a circuit for two 12-amp loads that will plug into separate 15-amp outlets. These will be the only loads on a circuit with a 30 amp breaker. If the first outlet is a 15 amp GFCI and the second outlet is wired in line downstream with the GFCI and the two devices operate simultaneously, will this put too much load on the GFCI?
You can't do that to begin with
You can't put 15A receptacles on a 30A circuit in the first place -- NEC 210.21(B)(3) says no to that plan, and for good reason.
So, rethink your plan (this'd work fine and dandy with a 15A MWBC instead).
Nope, nope, nope. You cannot put a 30A breaker on common receptacle circuits, for so many reasons.
Your 20A-rated GFCI cannot handle 24A anyway (12A of its own load plus 12A passthru). Use two GFCIs. Since you're using two GFCIs anyway, then as TPE says, use a MWBC.
Alternately, get 240V versions of these appliances, and wire this new circuit 240V instead of 120V, with NEMA 6-15 or 6-20 receptacles. Double the voltage means half the current, and that means you have two 6-amp devices, which is no problem for a 15A or 20A circuit.
240V NEMA 6-15 dual receptacle. Look familiar?
Alternately, install a dryer style circuit with 10/3 cable and a NEMA 14-30 receptacle, and have that feed a listed PSU.