Coming from a chapter who did do it - I have (all from my graduate program) 2 grandlittles and one great grandlittle who managed to successfully navigate recruitment and membership as graduate students. (There are probably more and I'm just aware of them).
It wasn't impossible and they managed very well and all of them are very appreciative of the opportunity and took a lot away from it. They are all still involved in some way as well.
Most chapters on my campus really don't take them to be honest, even if they are able to accept them. Which is a shame because I've never had any be a bad members -they have great GPAs, realistic attitudes and goals, and always pay!
I just want to offer the other side.