Not quite. There is no need to sign anything, what matters is if the EULA was included in the sale contract (so, the buyer was aware that the willingness of the seller to sell you the product depended on the buyer accepting those additional terms as part of the contract). On the other hand, if you do indeed sign an additional contract afterwards on your free will that limits your rights, that might very well be enforcable. But the point is that there is no legal necessity to sign such a contract in order to use the software that you have bought.