How long can I be suspended from a large grocery store with a union, before I can draw unemployment benefits?

If you are "suspended" by your employer that is a large grocery store operator where you are not drawing a pay check, I would go immediately down to your unemployment office and make a claim for such benefits. It is better to apply for such under the situation that you are writing about than not to.

Given what you have written, for all intents and purposes you are unemployed. After all, you aren't drawing a pay check from my read of your question.