<<Are Roman Catholic priests in demand now?>> YES very much so.
The faith continues to grow, however most families no longer encourage their children to become Priests, instead, wishing them to make money, be successful, and give them grandchildren.
After seeing decades of decline in the # of Priests, the Church has started to advertise and campaign more for vocations to the Priesthood. The Church is also making it VERY well known among Catholics that vocations are needed.
In recent years there has been a small up-tick in the number of Priests entering the Seminary, but still not enough.
So they are in demand, but things are getting better.
<<...would it be easier to "enroll" to learn to become a priest now?>>
Somewhat counter-intuitively -- NO, it is NOT easier NOW, then it was decades ago, or even a few years ago.
To the contrary, it has gotten HARDER. WHY?
In the wake of the sex abuse scandals, the Catholic church has invested more time and money into Psychological evaluations prior to accepting seminarians into the Priesthood.
Secondly, it takes more schooling and theological training then it did decades ago.
Lastly, if a candidate was rejected by 1 seminary, up until a few years ago, they could apply at other seminaries until they were finally accepted. From what I've heard, the Church has closed this loop-hole and NOW, if you are rejected on certain grounds from 1 seminary, then you are not accepted at any.