I didn't learn morse and I don't know anyone that has so my advice is don't let it distract you from your studies which will keep you busy enough. All I did was type up a list of the idents for all of the navaids I used during the IR course. I had these as a handy reference guide on my kneeboard. On my plog I wrote in the ones I would need on the day. After you have heard them a few times they tend to sink in anyway.
The "oldies" will be turning in their graves but I am afraid it isn't a skill that you necessarily need these days. The enroute charts all have the morse ident if you need to listen to them as do Jeppy plates. Modern aircraft that you are likely to be flying after your training all ident automatically and you would only have to revert to actually listening to the morse if you ended up with downgraded systems. In the case of the latter you would just pull out the charts and plates and check them off.