SpaceX gives the LEO payload of Falcon Heavy as 63.8 tons (presumably in fully expendable mode).
Orion, fully loaded with propellant, is about 26 tons. So LEO flight is doable, possibly even with booster recovery, but probably not with 3-core recovery.
I can't find specs for the ICPS stage that's going to be used with SLS, but it's a modification of the DCSS-5 upper stage used with Delta IV:
Those modifications include lengthening the liquid hydrogen tank, adding hydrazine bottles for attitude control and making some minor avionics changes to meet the design parameters and performance characteristics as needed by NASA to meet the flight objectives.
Falcon Heavy can lift a DCSS-5 stacked with Orion to LEO, from
from which point the DCSS can provide about 2960m/s of delta-v beyond LEO, which is not quite enough to reach the moon. Orion could use its service module to do the rest, but that would leave it with insufficient fuel to enter and exit lunar orbit, so that would be a flyby mission. (ICPS on the Block 1 SLS is supposed to put Orion on a very eccentric lunar orbit for EM-1; it's unclear to me if that configuration is capable of reaching low lunar orbit and returning, but that larger EUS for Block 1B certainly will be able to.)
Without a hydrogen-fueled upper stage, Falcon Heavy second stage could put the Orion into a GTO, but again Orion wouldn't have quite enough delta-v to both circularize there and return to Earth.
At this point, it's a toss-up whether a suitable upper stage could be adapted for use with a human-rated Falcon Heavy before SLS block 1 is flying.
Meanwhile, Delta IV Heavy can put Orion into LEO for development and shakedown flights, making it analogous to the Saturn 1B to the SLS's Saturn V.