Many american teams struggle a lot at Le Mans because european way of racing is totally different and even regulation are really different between ALMS and ELMS/LM. European teams have the same trouble when going to ALMS.
The problem of Dyson is that Lola is pretty sick atm.
I don't think introducing GTE AM class will creat problems tbh. In europe/WEC there are more customers for it than GTE PRO. Teams have to find the budget for PRO cars. In GTE AM, amateur drivers are paying for it and as there is a possibility to race at Le Mans, GTE cars and teams are really attractive to them and there is many gentlemen drivers for it.
It is basically the same in America with for example Seth Neiman or Bret Curtis. I think that some gentlemen don't want to race GTE in ALMS because the level in GT is so high that they can't win a race even achieve a podium. With GTE AM they will be able to do so and that will most probably attract them. Furthermore cars are cheaper as they were already used (IMSA Performance's chassis is from 2009, Prospeed was from 2009 aswell, and Flying still have some old chassis).