Only if you use a clean, unmodified NSP from the eShop on a non-modded console. Any unofficial NSP will be flagged by Nintendo’s telemetry, leading to a ban.
However, the Switch hacking community (via Atmosphere and other CFWs) allows players to dump their own cartridges. The shared NSP files often circulate specifically to allow Western players to load the game onto their modded Switches. Without these ROMs, the only way to play is to import a physical cart from Japan and navigate menus in dense Kanji. Battle Spirits CrossOver Switch ROM NSP UPDATE