"NO. If coded properly."

Plus the fact that after RI triggers an interrupt, you've got roughly the time it takes to receive the next byte before you have to service the interrupt. Upon completion of shifting in a byte, the shift register transfers the byte into SBUF, RI becomes set, and the input shift register is free to shift in the next byte, so you should have plenty of time to deal with the first byte. So, no worries, right?