No it wouldn't. Indentured servitude requires someone to be indentured, which is immediately in conflict with OP's correct observation that no one is being forced to work. They directly hinged their question on the premise that the workers are free to make choices.
OP's question regarding the free choices of previously unemployed workers is valid. Questioning why 1099 employment isn't "moral" as you put it is also valid.
> > People are not agents of free will, and any sub-utopic framework they have to participate in is immoral?
> This is a straw man argument to its core. No one is, or has suggested that all labor should be abolished unless it meets a utopian ideal.
Actually your response is the straw man here, because you have introduced and attacked an absolute (all labor) where one did not previously exist.
You're projecting the errors you yourself are making onto OP.