It depends. The issue is determined in accordance with the applicable law. Applicable law should be interpreted to include the law of the contract, the law of the jurisdiction at the seat of arbitration (if different), and the law of the jurisdiction of enforcement.
Arbitrability is important for enforcement purposes. Under Article II 1. of The Convention on the Recognition and Enforcement of Foreign Arbitral Awards (a.k.a. the "New York Convention"), an arbitration award is only enforceable if the subject matter is arbitrable. The New York Convention allows signatories to limit enforceability to differences arising out of legal relationships, whether contractual or not, which are considered commercial relationships. Both the governments of Canada (excluding Quebec) and the United States have done so through their registered declarations. Of the 172 States that have signed the New York Convention, 77 have registered declarations or reservations under the treaty.
Since enforceability is a key benefit of arbitration, arbitrability should be considered a threshold question when choosing the law of the contract, the forum for dispute resolution and when drafting the dispute resolution clause. Interestingly, the arbitrator(s) themselves determines whether or not the arbitration agreement gives them the jurisdiction to hear the matter. This is called the “competence-competence” principle, which was affirmed by the Supreme Court of Canada in Uber Technologies Inc. v. Heller,  2 S.C.R. 118, with a narrow exception.
Intellectual property (“IP”) rights are unique because they are mostly granted by a State. Some states do not allow the arbitration of IP issues at all (e.g. South Africa), or only allow arbitration of infringement claims and IP rights in contract disputes, leaving validity of IP rights to national courts. In Canada, courts will defer to the agreement between the parties when determining what can be arbitrated. In Desputeaux v. Éditions Chouette (1987) inc.,  1 SCR 178, the Supreme Court of Canada stated:
“The parties to an arbitration agreement have virtually unfettered autonomy in identifying the disputes that may be the subject of the arbitration proceeding.”
It is possible to exclude or carve-out IP issues from alternative dispute resolution in a contract, thereby ensuring that litigation is pursued for all IP issues. Alternatively, if the parties decide to include IP issues in their alternative dispute resolution clause, they could also consider whether that clause is accessible for post-contract breaches as well. In that regard, the risk of losses related to post-contract IP infringements could be mitigated through language in various terms of the contract, like the licensing, indemnity, liability, termination and survival clauses.