Is it possible to go active to national guard reclassing into 17c?

You can join the NG after you ETS

Reclassification to the MOS requires a particular time commitment after training is complete (which will take almost a year by itself. Once that obligation is up, you can try to get a slot at one of the NG units that has slots for 17C and depending on the state, many of them tends to only have AGR. If you are trying to reclass after joining the NG, you have to get a slot at a unit that has slots for 17C first and then go to training, which is less likely to happen because they'd be the ones you'd need to pay for the training, and the positions usually have a long waiting list of people trying to get in. You can always talk to an NG recruiter, but I suspect if you are accepted Active Duty now, if you attempt to get out prior to training and switch to NG, you'll lose your chance because they're trying to fill their needs and the NG in your state may have their requirements already met.