Surprisingly, no. All a "wallet" has to do is compute a signature using a private key. Then the resulting transaction has to be sent to a "mining" node (or the "mempool" of a group of nodes) and wait until one of them incorporates it into a transaction, computes fourty trillion hashes and then throws all but one of them away, and broadcasts the resulting signed block to the network.

Because there is no confirmation on sending bitcoin "into" a wallet, no action is required at all to receive and store it. It's only cashing out where it gets difficult. It also makes it possible to send to inaccessible or nonexistant wallets.