Yes, it is possible to do this. Pokemon of all levels are able to participate in Super Training. However, you should note the following things before doing it:
- The amount of damage, accuracy, etc. with the soccer balls your Pokemon throws it determined by its stats. Since a level 1's stats are so tiny, the training session will be very tedious and repetitive, and you will probably fail the harder regimens altogether.
- You can max out its stats at level 1, but really it isn't worth doing. If you could level up the Pokemon to a higher level and get decent stats, regimens will be easier and less repetitive to play.
And besides, because of the way EVs work at level 1, you would ness a ridiculous amount of EVs to get just one stat point. Of course this translates to the normal number at level 100, but it still doesn't make the regimens any less boring.
Learnt the first one the hard way. :/