Yes this is season for celandines. So their tubers have been dormant until recently and did not suffer any "mulching effect" of light exclusion. Likewise I am afraid any bindweed roots will be dormant and waiting… this is one issue of timing the mulch, with most perennials best mulched from now until say June.
However you may not have any other perennial weeds and yet you do need to trowel them out, hoeing makes little difference and they persist if not multiply. The tubers are hard to extricate but this dry weather will help. If you had a mass of them I would remulch and grow squash or potato, wide-spaced plants, through the mulch.