Is it possible to attend CCC while in IRR status?

Have you completed your service obligation? This may affect your ability to transfer. https://xtranet/usarc/usarpag/RequiredDocuments/Memorandums/Reassignment_of_AR_TPU_Soldiers_to_the_IRR.pdf
According to the HRC website it's not impossible to attend schools while in the IRR, but I found it extremely difficult because there is a lack of "command support". It was hard to a hold of anyone.
There are reserve units in Germany, Italy, and Korea - not sure if those would be close enough to travel to for drills …. there is also the option of IMA. IMA is a compact TPU status - they typically have all their drills in one month and you can choose to add on your AT and knock all your yearly training out at one time.
FYI- I am aware of at least 3 people that were passed over for promotion just because they were in IRR. I thought it would be less competitive (because you don't need a slot) but I was wrong. Something else to consider if your 2 years falls into your primary zone.

I think it’s the 7th Mission Support Command that has TPU slots in Europe. Mostly Germany, if I remember correctly. As for changing branches at CCC, it may be as simple as getting slotted in a position with the desired AOC. Then you should reflect as not “MOSQ.” Then the unit should have the ability to submit the ATRRS application for the required schooling on your behalf.

When you go IRR, you will be assigned a Career Manager. Are you looking at doing it Active Duty all at one time? Either way, you career manager is the one to get it moving.