Could the SLS block 1 reach orbit without solid rocket boosters, and if so, how much payload could it lift?
Fully fueled, the first stage alone has only an 0.77:1 thrust-to-weight ratio; it can't even get off the ground without help from the boosters, which produce more than 4x as much thrust as the core.
If it couldn't reach orbit in the block 1 config, could it do so with the Exploration Upper Stage?
EUS actually makes this problem worse, because it's a heavier upper stage -- all the delta-v in the world doesn't do any good if you don't have enough thrust to get off the pad.
According to some spreadsheet estimating, I believe that with the ICPS and an underloading of first-stage propellant -- say, 500 tons instead of its usual 894 tons of hydrogen and LOX -- it could get off the ground and reach LEO with about 22 tons of payload, which is no more than some Atlas V or Delta IV configurations can do. This would be wasteful, since it would be hauling propellant tanks that were nearly half empty at liftoff.
A shortened version of the SLS core would be less wasteful for no-boosters configurations; I'd estimate something like 31 tons to LEO for a 550 ton first stage + ICPS, or 40 tons to LEO for a 440 ton first stage + EUS. Those stages would be pretty stubby, around half the length of the SLS core.
These estimates could be off by as much as +/- 7% in payload.
I know the Atlas V and Delta IV can reach orbit with a single liquid first stage engine, so it doesn't seem like there'd be any problem with the SLS, which has 4.
All stages and engines are not created equal; the empty weight of the SLS core stage is four times that of the Atlas V and three times that of the Delta IV cores.