1 sat/byte transactions can also be mined especially on weekends when the unconfirmed transactions are usually low in the mempool but this all depends on the state of the network. Some weekends, the unconfirmed transactions can still remain high making your 1 sat/byte transaction low priority.
There is priority of your transaction and miners will choose the transaction that bring them highest mining fees.
In the other words, if two transactions with same fee at 1 satoshi/ byte.
- Transaction A has its size at 226 bytes (1 input, 2 outputs, P2PKH)
- Transaction A has its size at 260 bytes (1 input, 3 outputs, P2PKH)
Miners will prioritize to confirm transaction B because they will get more fees from it. Imagine when Bitcoin dipped to below $4k in February, you saw it but it does not mean that you actually were able to buy bitcoin at the price.