Not quite. The first sale doctrine says that there would be no violation of copyright for the user to sell or lend the software [1]. That doesn't clear non-copyright roadblocks that might be in the way. If the vendor's EULA attempt succeeds in forming a valid contract between the vendor and the user, the "no sale" clause in that contract would be such a roadblock, and would be enforceable.

As to whether or not the EULA will be a contract, the courts have been inconsistent on that, if I recall correctly. In a district where the courts have decided EULAs can be enforceable contracts, whether or not a particular attempted EULA is one will depend on the details of the particular case.

[1] I left out "rent" and "lease" because first sale in the US has an explicit exception that makes it not apply to computer software rentals and leases if those are for "commercial advantage").

This is why these "agreements" start out saying the software is licensed to you, not sold to you.