No. An expired .eth name doesn't affect wallet access. Your wallet, the funds in it and your private key don't depend on the name.
A .eth name is a label that points at your wallet. It isn't the wallet itself. Think of it like a contact in your phone: delete the contact and the phone number still works; you just have to dial the digits.
What stays the same
Your wallet address: same
0xaddress, same balance, same history.Your other tokens and NFTs: still yours.
Your private key: signs transactions exactly as before.
What changes
Once the name stops pointing at your address:
Payments sent to
yourname.ethstop reaching you.Apps that showed
yourname.ethfor your wallet show your0xaddress instead.
If the name is in its grace period, you can still renew it at the normal price, and nobody else can register it. See What is a grace period?