Yes of course, it's possible. For an idea of timetables and travel time look at planners, for example DB Navigator.

On top of the Eurail Pass you might have to pay seat reservation fees, mainly on high-speed and night trains.

Some advice in chronological order:

London - Paris Eurostar trains have very popular and there's a Eurail passholder quota. You should book ASAP for travelling over Christmas.

Paris - Zurich direct TGVs cost 29€ extra but you can save a bit by getting off in Strasbourg or Mulhouse and crossing the border by regional train. ;)

While in Zurich you might plan to explore the Alps so leave a pass day for it, it will be good value over expensive tickets.

Personally I'd remove a day from Munich and put it to Zurich/elsewhere closer to the Alps instead.

Munich - Rome takes a while but you get to cross the Alps. The last bit from Bologna takes 2h at high speed.

Rome - Amsterdam is barely doable in a day. You might want to experience a night train then! During the day travel to either Zurich or Innsbruck and board one there. Only a single pass day is required (the departure time is what matters). Book accommodation onboard in advance -> shared couchettes are cheaper than single/double/triple sleeper compartments.

Amsterdam -> London Eurostar trains are not running until mid-February due to engineering works. In the meantime change in Brussels.

Feel free to ask anything.

These links may be helpful too:

https://www.seat61.com/how-to-use-a-eurail-pass.htm

https://www.seat61.com/interrail-and-eurail-reservations.htm

Maybe doable again when the Milan-Paris TGVs start running again. Might be in March. It will still be a long day though.