Presumably it won't take all too long to reach page 300, so in the end it won't make much difference whether you start now or later.
Personally I'd say, don't sink too much time into learning kanji from the lists in Genki. It doesn't present radicals at all (the basic building blocks from which kanji are composed), even though knowing these makes it much easier to remember the characters. It also doesn't point out similar-looking characters (e.g. 年 <-> 午 <-> 牛, leaving you to figure this out yourself) or kanji that are composed from other kanji (e.g. it teaches 道 but not 首, even though knowing the second makes the first one trivial). Of course, you'll need to know the characters to be able to follow the lessons and do the exercises, but be aware that there are more efficient ways of learning them - like KanjiDamage and WaniKani, just to name a few.