Hi Felicia. As we are all Real Estate agents or associate brokers and NOT Attorneys, I strongly suggest you consult with your Attorney on this. You need one anyway to complete your purchase. Anything I might add here is experience based but anecdotal.
I believe you refer to a "Binder," where along with your written offer, financial statement and credit report, you leave a very minor deposit and sign off indicating intent to move forward to a Contract signing. Yes, you can always recind your offer any time prior to an actual signing of a Contract of Sale.
Every situation had it's own merits and negotiation is part of any deal to whatever extent. Timing may be an issue of any resultant consequences. If you recind your offer in writing through your broker or Atty before you recieve the countersigned Binder, I would see no problem there. If the offer is accepted and the binder agreement is countersigned it is conceivable that your binder deposit may not be refunded. Still, the agreement would have language that you would have read before signing it in the first place. Hence, the importance of a buyers Broker and an Attorney for this and other aspects of purchasing real estate. Good luck.