I've just spent the last week traveling between Manchester and Leeds for a conference.
The earliest I got the train was 7:20am and the train was pretty quiet, no busier than off peak. A train I got at around 7:45am was similarly quiet, so I imagine that 7am would be little different. The former journey was from Piccadilly, the latter was the fast service from Victoria.
Thus at the time you want to travel, based on my (limited) experience there shouldn't be a problem, a bigger issue is likely to be if there are already two or three bikes in the cycle storage space.
If you are coming back in the evening peak, then that WILL be rammed full, no matter what train you get between, say, 5pm and 6:30pm. I wouldn't like to try and get a full size bike on. i would advise traveling back after 7pm when it will be quieter.
One thing to note is that the peak demand seems to be from people traveling between Huddersfield and Leeds, so that is why it is quiet in the morning from Manchester, but really busy from Leeds in the evening.