Testing Heart Gold on a CycloDS Evo with firmware 1.55 at the time of posting. Able to save immediately after talking to mom, spamming enters/exits as I type this. Will update when necessary.
Edit: Game froze after several more Enters/Exits.
Edit Too: Testing now with 37 patch.
Edit Once More: 10 saves and 50 enter/exits and no freezing with 37. I'll do till 100 enter/exits and then start battling to further test.
Final Edit: Froze on 77th enter/exit. Definitely makes the game playable, provided you save often.