more or less, yes! you can watch it!! GO!!!
but it's great that you watched RTTT because they are chronological in real life history (RTTT is based on 1999 classics year and BoaNE on 2001. we do not talk about what happened in 2000<--guy who is always talking about it)
since you watched RTTT you probably get how the triple crown races work but i'll leave a glossary here for anyone on the fence and checking this question
classics year - 3 year old season, when most horses debut (some debut at 2, but the generation is defined by the 3 year olds. so pokke, tacchy, cafe and dantsu are from the 01 generation)
triple crown - once in a lifetime set of races that can only be done by 3 y/o (classics year). consists of satsuki sho, japan derby, kikka sho. you only get one chance, so if you miss them tough luck
japan cup - big race for the best of the best. can include overseas horses, so it's like the world's stage.
arima kinen - final race of the year, this is a huge deal