Concerns about Shakespeare's historical accuracy aside (and there are plenty of them), then it'll be hard to predict.
Richard was genuinely unpopular by the time of his deposition, and meddling with rightful inheritances was always something to rile up the Lords in medieval England. If cousin Henry isn't banished when John of Gaunt dies, then Richard will not be able to pull off his OTL stunt. Gaunt was the richest man in the realm, and Richard had simply taken the whole thing without so much as a "how d'you do". If it could happen to the LLancastrian inheritance, what chance did Lord Bloggs have of passing off his two bit manor with a couple of fields to his son, or Baron Generic of holding his castle against such an arbitrary king?
There's also a chance that if Henry is around, and malcontents are talking about him as the heir, Richard may decide to clarify who his heir actually is, which causes plenty of changes...