Yes, I'd definitely think so, but of course this depends on how many cities or areas you want to visit in all of these countries.
I only hope you are rolling in money because some of the countries you mention are pretty expensive!
I have travelled in Europe extensively, using public transport (mainly trains). When I was at University I took four trips. All of them lasted approximately a month. The first one was to England, Scotland and Ireland. The second one to Spain and Portugal (3 weeks). The third one to Italy, Greece, Budapest and Prague (5 weeks). The fourth one to Sweden, Finland and Norway.
So comparing that to your intinerary it seems reasonable that you can fit this into three months.
For long distance journeys I usually took night trains, as this saves both time and money that you'd otherwise spend on a night in a hotel.