With Schwartz not yet signed, there are some concerns on St. Louis Game Time and Lets Go Blues! that the Blues are running the risk of Schwartz jumping to the KHL. I don't think so. There are two documents that matter. The first is the NHL-KHL Memorandum of Understanding. It's a pretty simple document. This seems to be it in it's entirety.
NHL-KHL Memorandum of Understanding
1. The two leagues are to exchange data on any players who have existing contracts with KHL or NHL clubs. The data should include the player’s name, surname, date of birth, club, contract expiry date and his status. On demand of one of the parties, the other party shall supply a full copy of the player’s contract.
2. The KHL and the NHL are obliged to update the players’ contracts database every week with the latest information on any changes.
3. Both leagues should exchange their lists of free agents.
4. The KHL and NHL respect each other’s contracts. Both parties recognize and support the main principle: players under contract with a club from one league cannot fulfill any obligation to a club from another league during the term of the player’s contract.
5. In the event of any conflict or disagreement arising, both parties shall appoint their official representatives to hold negotiations.
6. Prior to such negotiations the parties undertake to provide all documents confirming or in any way associated with the player’s signing of a professional contract with any hockey club.
7. Toronto or New York shall be the venues for the negotiations between the official representatives of both leagues.
8. The NHL and the KHL are obliged to do everything in their power to reach a consensus concerning each player’s disputed contract status, including cases of labor conflicts, contractual disputes, etc. In the event of any failure to reach a consensus, each party reserves the right to act in the way it considers appropriate in such circumstances.
The key phrase seems to be "players under contract with a club from one league cannot fulfill any obligation to a club from another league during the term of the player’s contract." So is Schwartz considered to be "under contract"? Well, the other document that matters is the NHL CBA. I think I've quoted this section before, but here is the relevant paragraph from the NHL-NHLPA CBA:
10.2 (c) Players With Fewer Than Three Years of Professional Experience.
Any Player with fewer than the required years of professional experience set forth in Section 10.2 shall have no right to Free Agency except as provided in this section. Upon expiration of such a Player's SPC, the Club to whom the Player was last under SPC shall be entitled to make that Player a Qualifying Offer under the terms and conditions set forth in Section 10.2(a)(ii) above. A Club which makes this Qualifying Offer will have the exclusive right to negotiate with any such Player. In the event no such Qualifying Offer is made, the Player shall immediately become an Unrestricted Free Agent pursuant to Section 10.2(a)(iv) above
Schwartz is 22 but has only 2 years of professional experience as defined by the CBA. The Blues made a qualifying offer to Schwartz. They have the "exclusive right to negotiate" with him. He is not a UFA or RFA. Although it would likely require an arbitration hearing to be official, relative to signing with the KHL, I think Schwartz would be considered to be under contract to the Blues at this point.
FWIW, Ryan Johansen is not in the same situation as Schwartz. He is 22 and has 3 years of professional experience. He's a Group 2 RFA. He is eligible for offer sheets from other teams. Presumably, he is eligible for offer sheets from the KHL.