I would say so--how can the piece be together if you are playing in a random rhythm?
I speak as a percussionist--GET A METRONOME!! They are invaluable tools. Of course, should not be able to afford one, use an online one.
A technique my brother's teacher taught him was to stomp his feet slowly saying "QUAR-TER" and then quickly "EIGHTH-EIGHTH" to get the relationship that two eighths should fill up the time of a single quarter.
I think listening to a metronome will help with this (she personally doesn't want him using one, but I'm not a pianist so I can't help suggesting it)--use one that has a visual cue as well, a blinking light would be best. Start very slow and then gradually increase the speed. This will help you adjust to any speed while still getting the rhythm right. While gradually increasing the speed, gradually decrease the volume too. Eventually, go just along with the visual cue, and then turn that off as well.
There are also a lot of rhythm books out there, but I have no recommendations on those (others will chime in with those).
Another suggestion I've seen in books, on the forums, and from teachers is to CLAP/TAP the rhythm before hand, first with just the right hand, then the left, then together, then with fingers.
II. As in, second best.
Only lowercase. So not even that.
I teach piano and violin.
BM, Violin & Percussion Performance 2009, Piano Pedagogy 2011.