Wow....one search and here's the answer: Yes. They can't hold the ASI but they can attend the school and be tasked. Took me less than a minute of google-fu....including searching this board.
google.com > "sniper school ASI" > first link titled "Army Sniper Requirements"
This is a post from the user PJ24:
"Army Sniper" isn't an MOS. It is an ASI (Additional Skill Identifier). You're awarded the B4 (Benning school) ASI if you complete and pass the course.
You have to be an E-3 through E-7 and it is a requirement that you have the commanders recommendation. You also have to have a consistent 75% on your APFT and consistent experts in weapons quals, a psych eval and 100 GT score, vision correctable to 20/20 and your nose has to be sqeaky clean (ie, no getting into trouble).
It's a volunteer school, but not everyone that wants to go (and meets the qualifications) gets to go. You'll have to have some line time and have proven yourself a capable infantryman/marksman before they'll waste a slot at sniper school on you. You also need to remember that there are a thousand other young guys that have decided sniper school is cool so slots are hard to come by.
A lot of getting to go is just being at the right place at the right time, learning your job as an infantryman inside and out and being able to shoot that 40 on the range regularly.
Don't hang your hat on getting to go, choose an MOS that you'll enjoy even if you don't, the last thing you want to do is focus on schools because that's a sure way to get disappointed right out of the gate. Besides, when you don't expect it and aren't putting all of your eggs into one basket, it makes it all the more sweeter if/when it actually does happen.
Source: (*** -- Google: Military Quotes + Sniper Requirements)
Message was edited by: Jennifer Matteucci -- Removed due to AAS Policy Violation: https://forums.goarmy.com/thread/192791
Research it. Geez. Don't expect everything in life to be handed to you. I explained why you should research this on your own in your other thread. If you can't do basic research regarding what you want...you will NEVER get it. NCO's do not like spending their time doing what the Soldier should do for themselves. If they have the choice they will work with the Soldier who did the legwork before they work with the one who did not...especially when it comes to special schools.
ASI=Additional Skill Identifier
The ASI shows that the ASI holder has an additional skill in conjunction with their MOS. The ASI can be duty-position critical. If you are a 92F and don't have the H7 school....plan on working on a flightline or bag farm instead of spending time on the trucks. For Snipers....only 11-series and 18-series can hold the ASI. 19D's can attend Sniper school and be utilized as such, but the ASI is not awarded.
An example of how someone with an ASI's MOS listing may look. For a SGT, 92F, Parachutist Qualified, who has been to the Fuel Vehicle Course(H7)...their MOS listing would look like: 92F2PH7
A normal PV2 out of AIT would look like 92F1O