Kinda doubt because if it is in fact an Infernal Puzzle Box, then the box doesn't work like a Tardis (Bigger on the inside, Doctor Who), and originates from the Nine Hells. They're used to safeguard diabolical contracts between a devil and a mortal. Look up its full description if you'd like some material to enjoy speculating on. I find the more interesting question to be why does Shadowheart have it, seemingly prior to ending up on the Nautiloid? Suggests she's been to the Nine Hells before or directly/indirectly received/stolen it from someone who was.
Check
this little nugget and its comments for some more speculative food for thought ☺ï¸
I'm not sure why a contract would have a sentience of its own. The box expresses a desire to remain with the characters. It doesn't want to fall into the gith patrol hands any more than it wants to be taken by the Absolute, which the narrator tells us in the scene with the githyanki.
Regarding the infernal puzzle box possibility... maybe. I mean, it certainly seems similar'ish in nature, but it's worth noting that it's covered in gith script as opposed to infernal.
As to whether or not it's bigger on the inside: I don't know. But that aside, when we consider something like Dhourn's memory crystal, it's apparent that Larian is willing to slightly change things. In the adventure Out of the Abyss, they are called Stonespeaker Crystals and have the ability to offer visions of the past, present, and future.
