The short answer is no.

No, you do not have to be pre approved for a loan before making an offer.  However, commen sense and a competitve market dictate that it's a pretty good idea to be pre approved before wading in and making an offer.  Many Real Estate Agents (good ones) will insist you be pre approved before showing you properties. No sense in looking at properties you may not qulaify for.

Most pruchase and sale agreements have a finaincing clause that says you have "so many days" to make formal application for a loan (typically five in the Puget Sound Region).  So technically, if you see a house you like a lot and wish to move on, you can make the offer with the idea of making formal loan application after negotiating an agreement.  But in a Sellers market, where it is not uncommon for multiple offers, the Seller is going to accept the one that will net them the most, also consdering which is most likely to get the loan.  It is concievable that a pre approved Buyer that offers less may be considered over a Buyer that has not been pre approved, but offers more.

Plus, don't you want to have an idea what your loan costs are going to be?  Monthly payments, etc.