How long would you do this for? How many years? Wouldn't the AI's start breathing down your neck for not having any military? And by rush buy labs, you don't mean lease right? you mean just full price regular.
You're correct. I lease buy the labs on the longest terms.
The strategy usually culminates in wars in the early months of year one. (Not to be confused with year zero.) There are a couple of ways to handle it though.
First, I never give the AIs anything when they threaten me. If they want war, I'll be ready soon enough.
If I'm not ready for the war, which has happened a few times, I simply ignore it for the most part. Someone declaring war means little if they don't have planetary invasion researched. I just switch to a military buildup and attack when ready. I might build a few all attack ships to fend off any escorts that have troop transports with them if they've gotten that far. Any fleets without transports are just empty threats.
If I'm ready for the war, it means that my military strength was only a turn or two late from being able to prevent it. A quick buildup is usually enough to fend off any threat and diplomacy can net some big rewards.
Once the Spin Control Center is built, there's a several month window of opportunity where you can set up your attacks with near impunity. Take advantage of that window and you can wipe out an enemy in one turn. That should be enough to put you ahead of the other AIs or at least on equal terms with the most powerful ones.