Is there time progression in Alive or would I need to add a mod for it? Like does the clock go on like in real life or is there something in arma for it?

There is a time advance module in the editor. You can increase time so it is not 1:1.

I do not believe it is an Alive module, but part of the editor features.

I'd like to use this in conjuntion with a "rest/sleep" function, so my platoon/squad don't pull 24hr shifts every day of the campaign.

I use a mod called 3den Enhanced, you only use it while making the mission, but it adds UI based controls for a lot of built in ARMA functions,

Setting the time acceleration would one of those functions

We normally run at 3 x speed for our missions. Just place the time acceleration module down in the editor and change the speed factor.

Im not looking for real time Im looking for like 20 minute nights

Global time acceleration is easy, as mentioned (clock time, game still plays "normal"). With a little scripting you could probably get exactly what you want. Eg, change the acceleration rate at night, either done at a certain time, or by user action. Or, you could just skip to a specific time, again passively or via user action. Eg, quadruple the passage of time at 8pm, return to your original setting at 7am, or, jump directly to 7am either automatically at a certain time, or have a user action to do so so you can have some night time, but jump ahead when you've had enough.

Don't have something on hand, but the scripting commands should be fairly straightforward: Time = XXXX to activate at a certain time, either skip time or setacctime to either skip X hours, or change acceleration rate.

20 min nights? Jeez at that point why not just pause time altogether

To elaborate on what BvB said, I use the following code to make night time pass faster than daytime.

if (!isServer) exitWith {};
while {true} do
{
    if (daytime >= 17.40 || daytime < 6) then
    {
        setTimeMultiplier 12 //for night time
    }
    else
    {
        setTimeMultiplier 4 //for day time
    };
    sleep 120;
};

Saved in "time_cycle.sqf".