But do have your realtor check with the listing agent --- how close is the current offer to the point that the contingency will be released? Is it contingent on the buyer selling his own house? Contingent on getting the loan approved? Contingent on having inspections and repairs done?
If the listing agent is still iffy, and still looking for back up offers, then consider that your go-signal to move forward with an offer (remember, the seller can reject, counter, or accept your offer as back up --- so that's another thing you should know).
It is not at all unusual for accepted offers to fall out for diffrent reasons. The buyer: changes mind; can't get financing; doesn't want to do repairs; can't get credits for repairs or closing costs he asked for; found another house he likes better; has a disagreement with the seller. In my case, I've had a buyer lose his job the day he was supposed to clear the contingencies!
So yes, anything can happen. Good luck!
In the current market many contingencies are not being satisfied and deals are falling through. However if you do put in a backup offer and it is accepted, you will have to wait for all of the contingencies to either be satisfied or not before you will know if you that you have a pending contract on the home. This will probably tie you up and not allow you persue other properties if something else becomes available in the meantime.