Will the collection agency favor me if I agree to repay debt before asking for debt validation?

Sorry but your decision might be fatal. As ditchdebt said earlier, what if the collection agency is a fake one? You'll loose money due to a scam.
Always ask any debt collector to validate the debts, it is your right to make sure that the debt belongs to you.

Of course, they will favor you if you agree to repay debt before asking for debt validation. Why wouldn't they? Debt collectors want money. That's it. But what if the debt is not valid? You would end up paying a debt you don't owe. It's a very bad idea.

Will they agree to settle the debt for a better offer?

If you know that the debt is yours, then only you can go for this option, that is, negotiate without asking for debt validation. However, if you have even 1% doubt, I would suggest to ask for debt validation. Why will you agree fearing that they will not agree to your offer? Instead, be sure and then start negotiation. It will also make you confident to talk to them.