Whether you're paying cash or looking for a mortgage, you certainly want to have some idea of value before making any offer.
To answer your question -
No, I wouldn't suggest paying for an appraisal now, before putting in an offer...why spend hundreds of dollars if you don't know you will be buying the home?
You can put a contingency in your contract that allows you to have an appraisal done at some point AFTER you reach an agreement with the sellers.
You can require that the house needs to "appraise" at the number you are offering, or, if it appraises for less, you can renegotiate the number with the seller....or walk away.
If you have an agent (and I am going to guess you don't), he or she would do a market analysis for you so you can get a sense what is happening in that market.
You will see the current active, competing listings......and those that are pending, as well as recent closed sales (we call them "comps").
Once you have that information you will see what similar homes are selling for, and be better informed before making a decision on your offer.
If you're doing this on your own, without the benefit of an agent's advice - well then.....best wishes............