There were 704 episodes of Star Trek not including TAS which would bring up your total to 726. Assuming the average length of all episodes with commercials removed is 42 minutes that gives us 492 hours 48 minutes or 508 hours 12 minutes of non-stop TV Trek depending if you're only counting TEH CANON!
Counting the movies' total length of 1144 minutes that would add an additional 19 hours 4 minutes to give us a grand total of 511 hours 52 minutes (21 days, 3 hours, 52 minutes) to 527 hours 16 minutes (21 days, 23 hours, 16 minutes).
As of today, there are 125 days until opening day. You'd have to watch on average 4 hours, 5 minutes, 42 seconds per day to watch every Star Trek episode and movie.
Of course, that's not counting any special relating to the series. But good luck!