Can a 74AHCT IC be a drop-in replacement for 74HCT IC
The 74HCT04 is plenty fast enough (~25ns) for 38.4k transmission speed (26usec/bit). 8ns vs. 25ns will not be noticable, though as analogsystemsrf points out, it may cause more ringing that may or may not be a problem. 

The main difference you may notice is that the AHCT part draws about double the supply current when the inputs are at ~3.3V (~1.5mA per input at ~3.3V vs. ~0.75mA per input at ~3.3V). 

Clamps do not come into play when the IC is powered from +5 (and it is not specified for 3.3V power). The HCT has diode clamping to Vcc.