With this timetable should I wait to see what the Officer boards say?
If you want to be an officer, going through the 6 month to one year-ish application process is shorter than the years it will take you to build an enlisted resume that will get you a strong endorsement for OCS. This assumes you can sustain yourself in the interim and you will not be over the age limit by the time you commission.
Are my hopes of going in directly as an Officer realistic?
Yes, although your courses of study probably don't make you eligible for nuke SWO or subs.
What are the barriers and circumstances to becoming an officer once enlisted?
Mostly institutional inertia -- the Navy already has you employed in a job it needs and a large civilian applicant pool for officers, so now you have to convince them to let you 'convert.' This generally involves being a top-notch Sailor, qualifying early, with good evals, etc. which is ironic because your credentials without any prior service are sufficient, particularly if you crush the ASTB.
Depending on the group of guys you become friends with, they might not think it's 'cool' to go 'khaki' and could convince you of that, too.
Will being a Nuke increase my chances to become an officer once enlisted?
No. There is an opportunity for nukes to apply to STA-21 for SWO/sub nuke in the enlisted nuke school pipeline. This is a collegiate commissioning program and you are not eligible for it because you already hold a bachelor's.
You can theoretically apply for OCS at any time as an enlisted Sailor, provided you are not within 1 year (IIRC, if not 1 year then close to it) from transferring to another command. Since you will not be stationed at a command longer than 6 months until you get assigned to a ship or sub, you are talking about 1.5 years minimum before you can apply. It will be difficult for you to get a strong recommendation from your CO until he knows you, which typically takes time, requires you to be qualified, and requires picking up highly visible collateral duties. As an enlisted nuke, it takes 18 months-ish to be senior in-rate qualified.
Put it all together and you're talking 3-4 years of enlisted service before anyone will seriously endorse your OCS package as a nuke.
I had a guy (non-nuke) show up to the boat and immediately put in an OCS package as an E-3. He went dinq because of the time spent applying for OCS vice working on qualifications, and was not well received by his division and eventually the crew. He also didn't get selected. A small sample size, but you will generally be expected to master the basics of your rate before you pursue any additional professional goals outside of that.