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.
Please note that during the Cycle 13 call for proposals the web based OT will be available for Cycle 13 proposals only. Any Cycle 12 DDT proposals should still use the desktop version of the OT found on the DDT proposals page.
Related documents:
"Director Discretionary Time (DDT) Proposals" section in Proposer's Guide