If one can learn only 1 language due to time and job constraints, would Perl be the right choice?

I think Java would be the most employable if you need a job, but you can always abandon your family, job, personal possessions, time spent creating nodes on what language to learn to make more time for perl learning. If you add up all the time spent waiting for the jvm to start your program you can read some perl books

Since the situation you describe is not possible it is not worth serious consideration.