Do Army 35M and 35P get to deploy?

The Army deploys units. You train, deploy, and redeploy with your unit, regardless of MOS. There is no individual filler system. The Combatant Commanders request Forces and the Joint Chiefs source these requirements with a Joint Capability. The services get handed a requirement and the fill it, in most Army cases through FORSCOM.

Intel work is a lot of reading, writing, analysis, and interpretation. You may do this while seated at a flat surface, you might not. You prepare briefings and deliver briefings because commanders need your products to make decisions. Intel work is not a self licking ice cream cone. You will find yourself in command posts, command tracks, SCIFs, and as it applies, in the field. You will not be Jason Bourne. You will pull Guard duty and other force protection details like all other soldiers.

Listen young buck, you have a lot to learn, and your time will come. Just understand that for every infantryman deployed it requires close to 70 support Soldiers. How do you think the ground pounders and door knockers get all of their ammo, food, fuel, supplies to accomplish their mission? i have seen discussions in here that talked about the most important MOS. The answer to that is ALL of them. Now their will be pride in each MOS, and that is a great thing, its what makes our Army traditions so strong. But in reality, we couldn't fight and win our countries wars without it being a TEAM. No one is more important than the other. All pulling together in the same direction on the same rope. As an 88M i relied on those "stuck behind a desk" to give me and my troops valuable intel on the roads we were preparing to traverse. I relied on my maintenance team to check and double check that our vehicles would not break down in the middle of some god forsaken place. I need ammo and i needed food, and i needed fuel, What i am saying is that you need to find a job that intrigues you and that you want to do and feel you can make a difference and take pride in whatever MOS you choose. Because if you are not pulling the same direction on that rope we are all screwed. Dont be in such a hurry to deploy, you might not like what you see.

Stay in long enough, you'll probably deploy. To answer your question, yes, these other MOSs can deploy. I can't say WILL as there is always that chance that they won't. I've known people with 35 years of service and never deployed. I've known people with 10 years of service and deployed 5 times. It boils down to your unit and what deployment cycle they are in.