RED DAWN!!!! Wolverines!The last thing the military is going to do in the event of an invasion is wait 3-12 months to respond so that they can take conscripts such as your self and go train them.
No. The response would be immediate. If we're talking a domestic invasion the existing military on US soil (to include the National Guard) couldn't handle, the government would not draft.
The government would activate the unorganized militia; a general call-to-arms for all able bodied citizens. Rally points announced, hasty leadership set up, and immediate action taken.
So it's kind of silly to say you would join if we were invaded. Once the foreign army is on our soil, it's to late to ship off to boot.
If you don't want to join the service, that's fine. No one will think less of you. But if you want to be ready to defend your country from invasion without joining the service today, then prepare yourself for the roll of militiaman. You don't have to become a survivalist or anything like that, just stay in shape. If you have a medical problem, no problem, just do what can do. Certify in first aid and have a basic kit in your house (IMO you should do this anyway). Be ready to go a few days without utilities. And of course, own a firearm; shoot it, know it, love it.