Hi,
Tricky situation here. It's feasible but not sure this is the best way really, as I don't really have a serialization system for Arrays to become strings ( and back to an array) easily.
what I would experiment with is "easy save" add on to arrayMaker, it allows you to save in the playerprefs as a key, since the player prefs are strings, then you could simply use that content as is and send it to google. with easySave addon, you can seave an array with one action, so it will be easier for you then trying to do that manually.
Doing it manually will mean you have ti iterate trhough all the array and build a string from it, and when you get the string from google, then trouble starts... because you have to split the string, and populate back an array. If you are new with all this, I would not recommand this as a first exercice really.
-- I think arrayList will be fine for your case, but if you use hashtable then you can express each int with a key, which is more meaningfull.
Bye,
Jean