Yes. A Director Discretionary Time (DDT) proposal for the current cycle can be submitted anytime during that cycle. One important thing for the DDT proposal submission is that OT for the current cycle should be used (even when OT for the next cycle is released). OT (and other information) for DDT proposal submission is available on DDT proposals page.
"Director Discretionary Time (DDT) Proposals" section in Proposer's Guide