If I arrive at my unit after they've left on a deployment, will I still go?

It depends; if he/she have an MOS that is required forward, late Deployment it is. However if the unit has all required personnel and reached force cap, rear D it is. Too many variables. Besides, if they joined during a time of war, they can expect a little rotation.

It is at the unit's discretion

Your friend will have to contact his gaining command to find out. Every command have their own way of doing this when a Soldier arrives after the deployment begins. My last unit sent everyone that came in up until 90days before re-deployment. So if your friend want a definite answer, he would have to contact his new command. Good luck.....

Tell your friend to sign up for Rallypoint.

The SM will deploy if needed. The unit should let the Soldier know before he departs on PCS. Some Soldiers elect to leave their families at the old duty station or near their family since they will deploy shortly after arriving at new duty station. It could be as quick as two weeks depending on any training requirements; SRP and equipment draw.

Will all depend on whether or not they need them to fill a position down range or not.

My second deployment, I arrived to the unit 2 weeks after they had departed. I was the senior enlisted in my Company and promptly became the acting 1SG.... For 4 weeks until I, myself, got on that shiny bird.
My last unit, I arrived 2 months BEFORE they deployed. But their deployment team was already set, so being the senior enlisted... I promptly became the Rear-D 1SG, and remained in that position until they returned, at which time I dropped my packet and retired.

It's a crap shoot. If it is a long deployment (9+ months) and you are arriving only a month later AND are up to date on required training, expect to be on the very first bird out. May not happen, but go with that expectation. If you arrive with less than 3 months left in the deployment, chances are very low that you will be sent forward. Could still hapen, but not likely. In between those two extremes, it's anyones guess. Well, actually it is the Commander's decision (with advice from S1), but you know what I mean.

With COVID this answer can be tricky depends if you are Mission Essential, how long they have left, and if you are filling a critical MTOE slot with someone leaving or PCSin themselves. I would just plan as if you are and be thankful if you don’t, unless you want to deploy.