If the company seems to be OK with remote employees, I'd assume you'd be fine to ask, no harm in finding out regardless. Some managers might not like it, which is why I left my first company, as I was told by my manager we can talk about being remote in a year.... No thanks :P If they won't grant it immediately, which is understandable, don't settle for "we can talk about it later", have some type of measurement and plan to get to full remote. I had this occur with 2 separate companies...
The 2nd company I joined had an hour and a half commute. I would go in once or twice a week when I first started which is what part of the deal was when I joined. Most of my co-workers were in that office, but my primary partner/senior was 2 hours from the office himself, so he also went in once or twice a week. I basically started to only come in when I had an important meeting, and would go weeks without being in the office. I'd recommend having a conversation around it prior to you doing that, as I was in a very flexible position.
I eventually asked to be full remote, and got the green light. At that position it didn't make much of a difference as I didn't even have a cube near my team and many of the resources I worked with were spread around different offices globally. The only downside was that I didn't seem to get any of the "unofficial" communications in the team, which made it harder to stay in the loop.
The first company I worked for a couple years, left, and came back as a full remote employee from the get go. I had worked in the same department but a different role prior to my departure so I had a good reputation. It helps to know people prior to going full remote, as you know who to get a hold of for what you need done, as sometimes an IM or email to the right person can save weeks. You kind of miss that at a big company when remote, or at least develop those contacts slower.
I'd start by bringing it up and working from home a couple days a week to get a feel for it and your team use to it. Personally I'm way more distracted in the office but it's more than just you, it's your co-workers as well that need to be able to handle it.
One aspect I noticed is when I'm remote, I'm usually west coast. Most days for me I'm logged in by 6 or 7 AM, for others they might not like that, but I like being behind, as nothing really picks up at the office til 9 anyway, and I'm able to have more daylight to do stuff after work. That won't apply to your case, but that's another thing for others to consider.