Could sloops lead groups of smaller escorts?

Could a sloop serve as the command ship for early corvettes and other small escorts?

Yes. Its greater size and capability often made it the command ship unless a destroyer was present.

The sloop's relative size mattered inside a mixed escort group even when it remained a small warship. Sloops were somewhat larger and more capable than early corvettes. That made a sloop a practical command ship for a group of close escorts. A destroyer, when attached, would normally take the senior role because it brought greater capability and command weight.