This depends on current workflows and coordination between ProQuest and Harvard Library related to depositing, processing, and cataloging. The library or your academic department coordinator can find out and tell you where the thesis is in the processing workflow.
Once approved and submitted by the department administrator it should only take a few weeks for the work to show up in ProQuest and in DASH, it may take longer to show up in HOLLIS.
**If in the future you need a print copy of your thesis you can obtain one from ProQuest for a fee.