No, not without an agreement. Copyright arises with the maker, and it only passes to you when it has been transferred in writing. A paid pitch fee changes nothing: it buys participation, not rights.
What that means in practice
A concept, a text, a design or a film treatment from a pitch remains the property of the agency that made it, even if you paid for it and even if you liked it. Using it without permission is an infringement, and in this market the chance of being noticed is very high: everyone knows everyone, and a campaign is by definition visible.
There is a second layer. An idea as such is not protected, its execution is. That line is vague enough in practice to cause an argument you do not want, and sharp enough to lose.
What to settle in advance
Put it in the pitch briefing, in one paragraph, deliberately choosing one of these three:
- The work stays with the agency. The default situation, and the fairest. What is not chosen goes back with them.
- You buy an option. For an amount named up front you may later use a proposal that was not chosen. Clean, because both sides know where they stand.
- Rights transfer on payment of the fee. Defensible when the fee is genuinely scaled for it. Then say so explicitly, otherwise you are buying three teams' work for a symbolic amount.
What you must not do is leave the chapter out. Then the law applies, and it stands on the agency's side.
The grey area where it usually goes wrong
Not the literal reuse of a campaign, but carrying "the direction" over to the agency that did win. That happens more often by accident than on purpose, and it is why a good briefing states what happens to the proposals that were not chosen.
This is a general explanation and not legal advice; have a contract reviewed by someone qualified.
Whether that chapter is in your briefing is one of the things IKAg's briefing analysis checks.
See also: what belongs in a pitch briefing and who owns the work when you stop.