No, not as long as you use a Battle.Net account you associated with the game
Also, Battle.Net prevents you from logging in from multiple locations with the same account, so you can't even create an unwanted situation
I don't play a lot of 3v3 and 4v4, but I would imagine the later tech transition is in part due to the much larger army you can bring to bare in early stages (having 4 people to draw on). I'm not sure how to help with that, but I can give you the 1v1:
Tech transitions should be part of your overall strategy. If your strategy is: Speedling into Infestory/Baneling into Ultralisk (the TLO ZvT), then you have clearly defined goals as to when to tech. You know that you'll have early harassment with speedlings, you switch to Baneling/Infestor as he starts to get Medivacs for his MMM, you'll upgrade melee damage, and once he gets his factory up and producing you'll move to Ultralisks.
Day9 once said "every [good] strategy has a beginning, a middle and an end." This was true even at the beginning of Beta when Zerg players went just Roaches. The strategy then was: I'm going to open Roaches. For my midgame I'm going to get Upgrades, Roach Speed, Burrow and Tunneling Claws. For my late game I'm going to get Roach HP Regen while unburrowed (since removed). Its not hard to see why people thought Roaches were overpowered at the time, but the key thing here is that even in this simple case he has ideas of when he wants to tech; its part of his core strategy.
This is not to say you won't have to adapt to what your opponent is doing. If your strategy is the TLO ZvT hellion harassment, maybe you build some Roaches before teching to Infestor. However, the key to execution is knowing that even before you've completely shut down that harassment you need to be upgrading your lair and getting Infestors. Just because you adapt doesn't mean you have to compromise your strategy.
I'm going to give you one last example: Terran MMM, because its actually well defined:
- I'm going to wall off and open 3 Rax
- Once I have a nice clump of units I'm going to expand
- My mid game is going to be getting Stim and Medivacs
- Once I have a sizable force I'm going to start breaking map control
- For my end game I'm going to add on factories and start pushing siege tanks.
The reason MMM is such a popular build is that is very easy to do and it has a very nice mid and late game transition. Once you have your 3 Barracks you think about Expo. Once you have Expo you go to Medivac for your Stim. Once you've moved to late game you're backing up with Tanks. At all points you are strong, and at no point do you stop using the unit producers you currently have.
Best Answer
Setting to busy (or away) is the best you can do. Your friends should honor that. Their IM system isn't extremely mature yet. Maybe they'll add features like this in time.