Cheap ERC20 Transfer to L2?

Is it possible to cheaply transfer an ERC20 token to L2? For example, I am thinking enabling Shib hodlers to use it for tipping or purchases.

SSTORE[x] = 0 refunds 15 gas so hypothetically, SSTORE[my Shib balance]=0 returns 15 gas. If you batch a bunch of these together and then use an L2 commit (which IIUC can be very cheap), could the cost be made trivial?