I would say that it is possible:
The one catch will be that the SELLER will be able to give you a "Notice to Perform" if they receive another offer.
It is a very tenuous way to do it, and stressful for both parties.
The only way I would recommend it for you, is if you found a house that was "to die for" and you had to have it.
Otherwise, consider that there will always be another house.
There would be no advantage in having the early offer; you wouldn't be saving any time or money.
Good luck and may God bless