Short answer. Yes. Rule 19, Section 1 of the Rules of Court directs the court to consider whether the intervenor's rights may be fully protected in a separate proceeding when deciding whether to allow intervention — so a court can deny leave to intervene on that basis, alongside considering undue delay or prejudice to the original parties.
What the law says
The court shall consider whether or not the intervention will unduly delay or prejudice the adjudication of the rights of the original parties, and whether or not the intervenor's rights may be fully protected in a separate proceeding.
Rule 19, Section 1 — Who may intervene. Read the full provision →
What the law says
may, with leave of court, be allowed to intervene in the action
Rule 19, Section 1 — Who may intervene. Read the full provision →
The separate proceeding factor
Rule 19, Section 1 directs that the court shall consider whether or not the intervenor's rights may be fully protected in a separate proceeding in deciding whether to allow intervention. This means a court can, and is directed to, weigh whether letting you pursue your own separate lawsuit would adequately protect your rights before it grants you leave to intervene in the existing case instead.
The other factor the court weighs alongside it
The same sentence directs the court to also consider whether or not the intervention will unduly delay or prejudice the adjudication of the rights of the original parties. These two considerations work together: even if your rights could not be fully protected elsewhere, the court still weighs that against the disruption your intervention might cause to the original parties' case, and vice versa.
Intervention requires leave of court, not a right
The article frames intervention as something a qualifying person may, with leave of court, be allowed to do, rather than an automatic right. A person with a legal interest in the matter, or in the success of either party, or an interest against both, or who would be adversely affected by a disposition of property in the court's custody, is eligible to ask — but the court's leave, weighed against the two factors above, is what actually decides the outcome.
What this leaves to the court's judgment
Rule 19, Section 1 identifies the factors the court must consider but does not itself set a fixed rule for how those factors are to be weighed against each other, or how strong a showing of adequate protection elsewhere is enough to justify denying intervention. That balancing is left to the court's discretion on the specific facts of each case. What the rule does fix is the checklist: a denial resting on the availability of a separate proceeding rests on a consideration the rule itself names, not on a ground invented for your case.