Can an account which has never held ETH, receive ERC-20 tokens? Can an account with no ETH, be used to hold tokens long term?

I understand that ETH will be required to pay gas and that these tokens couldn't be sent anywhere until ETH was sent in. Please let's just skip that part and move to the question I asked. I already know ETH is required to pay gas.

So say I create a new ETH account on my Ledger - a fresh account with no history of any kind. And I send 100 USDC to that account. What happens now? Is that going to work fine? What if I do nothing for a year (including sending no ETH), still working fine? USDC will still be there and able to be transferred (as soon as I transfer some ETH in).

Does this work the same for L2's? Like can I do the same thing on Arbitrum or Optimism or Polygon? Send tokens in with no regard for whether I have any of the gas paying token? And hold tokens long term with no regard for whether I hold any gas paying token?

I repeat for the third time: I fully understand that gas will be required to send the tokens out. So no need to explain that part.