Sure. You can pressurize the first, disconnect, pressurize the second, and then go get your splitter and reconnect all. No reason not to. Just get the whole thing connected properly as soon as possible so you can enjoy your brew.
Personally, I would not leave the party taps connected. Like you say, they are sensitive and a possible accident just waiting to happen.
Do Not leave the party taps attached. I lost a full get of a hard spiced cider because of this all because I was lazy.
I consider it a lesson learned. The next day I picked up the materials to build a collar and ordered all needed parts to hook up 3 stainless perlicks and a nitro tap.
I just set up my system and I bought two regulators. On the back of your regulator there is high and low. Just connect your regulators from high to high. Then you can enjoy two kegs at the same time and you can force carbinate one beer at 30 psi and have the other keg at serving pressure 10 psi. It cost a few bucks but you will love it.