I'm already in the reserve, training to be an officer. So, yes, I would. It doesn't matter that we're surrounded by reds or that our government is also red. I would fight to save the people from the oppression of the Big Bad Bear or the Red Chicken, to give them a chance at happiness.
We've experienced freedom briefly in the last couple of hundred years and if we fall once more to the enemy, we're never really going to stand up again. The Soviet regime did irreparable damage to the national spirit and along with all the other terrible events that happened before, has left our economy devastated and us all cynical and melancholic - a broken people in a slowly deteriorating nation, so to say.
And if we were to strike back with a vengeance to take back all that we've lost through treachery and underhanded means of other nations, then I would happily be at the forefront, leading all of my volunteer engineers to victory or demise.
If it were a traditional invasion towards a nation that didn't do anything to us, I would disagree and I'd make it known. Probably, I would just get transferred to Homeland Defense.
Now if there was a civil war... I'd go lead the revolutionaries. Nothing like fresh air to clear the stale smell of corruption, anti-innovation policies and the Reds. Bloodless, of course. The government would be too spineless to do anything.