No. The fork has to match the headset at both the crown bearing (1-1/4") and top bearing which fits 1-1/8". that's what's meant by a tapered headset.
If you're set on a standard 1-1/8" fork, you might find a special headset made for the application using the larger 1-1/4 lower bearing to fit the frame, but with a smaller 1-1/8" inner race (crown race) to match your fork. Or there might be an adapter shim made (haven't searched , so I don't know) made to enlarge a 1-1/8" fork's crown to the larger 1-1/4" nominal dimension.
Cane Creek is the major player in the tapered headset world, so you might start by checking their site or calling their customer service dept.
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