Dometic specs for a 13.5K AC are a 20 amp breaker and max. 24' of #12 wire. Not sure what Air Excel specs say for wire.
Someone pointed out the other day that wiring in a house is #12 ga. with 20 amp breaker but the receptacles are 15 amp. If that is the case, you *might* be okay. Check the breaker in the panel and the wire gauge.
AC units have a starting inrush current of about 5-6 times the running current and voltage drop can momentarily be very high. See Dometic manual
here.You may get the AC unit to start but damage is cumulative over time. AC units, unlike just about everything else, draw more current when the voltage goes down. You may have gotten the AC to start but the voltage may go down afterwards and at some point it will trip the breaker. Happens often in GGs. You may get the AC unit to start and it may *seem* fine, but damage is cumulative over time and it can die some day for no apparent reason. Even if you have #12 wiring in the house, you won't know how long the overall run is back to the panel. Then you have not only the length of the shore power cord, you've got #12 from the converter/panel to the AC unit. You could easily have over 100' of wire back to the panel, leading to higher voltage drop.
Nominal system voltage in the US & Canada is 120 volts, not 115, 117 or 110. If you look at the Dometic data, note the AC unit is rated at 115 volts. This is done on some motorized equipment on the assumption voltage will slightly less at the terminals at the motor(s) due to voltage drop in wiring. It does not mean 115 volts at the panel in your house is okay. You would be wise to get a plug-in voltmeter for inside your camper. Note that voltage can fluctuate throughout the day or go down in warm weather due to neighbors all running AC units in their houses, and can be worse at dinner time. The voltage *could* drop significantly when you aren't there to watch the voltmeter.
Pitted and dirty plug blades can cause resistance creating not only heat, but adding to voltage drop. Make sure your shore power cord and adapter plug blades are kept clean and shiny and never plug in when the power is on (shut off a breaker).
If you want to follow simply the "it'll be fine" advice without looking at tech. facts, it's your call and some day, your $$ if it fails.