Correct, for polling, FIFO or non-FIFO makes no difference. Bit 5 or LSR register indicates THR register is empty or not. In FIFO mode, this bit just tells whether the FIFO is empty or not (So does Bit 6 of LSR, but this also indicates whether tx transmission is complete or not).
By polling, it is not possible to know what is the current depth of the tx FIFO.
In some UARTs, there is a special THRE (Transmit Holding Register Empty) interrupt mode, which if enabled, switches the functionality of LSR[5] to indicate whether tx FIFO is full or not. This is helpful, since we can continuously write to the tx FIFO until this bit becomes 1.
For data reception, whether or not in FIFO mode, LSR[0] indicates whether data is available for read (irrespective or whether it comes from FIFO or RBR register) or not.