will the pro peak power supply 13.8v 8.5a work with the duatrax ice charger

Yes, it will run teh charger and as long as you're not charging over 7, maybe 7.5amps, it will work. You won't be able to use some of the other features like motor breakin or powering a lathe though. I believe the charger needs 12amps to for those features.

I ran mine with a 12a supply while DTX recommends a 15a continuous supply to make the Ice fully functional. ProPeak makes a 20a supply which is one of the supplies I'm using now. It would be money well spent if you could swing the bigger supply. This would make the supply viable for your next charger when that time comes.

Your charger is 120 watts max (on non-impulse 4-step) and your ps figures 117 watts. Theoretically it will all but max out the charger.

Many ps will do above the rating , more of them won't. Ultimately you can do any chaging job up to a point where the ps drops below 10.5 volts or kicks off from overload. The charger will turn off at 10 volts or less. A good guess is that you can do any job up to around 100 watts.

100 watts can be 12 volt output at 8 amps or 20 volts x 5 amps. To put it another way, the ps may not cut it at 5 amps or it may do just fine at 8 amps depending upon the output voltage (battery voltage)

Yep. The ICE uses a switching power supply internally, must consider the battery voltage. In general one can’t just say it will or won’t do X amps without considering voltage. For example I highly doubt that supply would allow you to charge a 4S lipo at 7 amps, at the very least not reliably.
Same thing for the motor break in & lathe functions, need to consider voltage.

Back to the OP, what batteries are you (& plan on) charging, at what rate/amps? Other functions?

Here's 2 identical chargers doing 100 watts (the input current is identical on the input)

Second pic is the same two doing 120 watts.

15.85 x 6.3 amps = 100 watts
26.3 x 3.8 amps = 100 watts

26.67 x 4.5 = 120
15.76 x 7.6 = 120