This would have made a lot more sense with a human character driven semi-insane by loneliness with some sort of protective equipment.
Neither Ash nor Bishop cared about longevity. Why would this synthetic? Especially as it/she could just need to plug herself into the ship's reactor for power, go temporarily dormant or simply copied/transmitted its memory and code, in order to effectively 'survive'.
Why did the character care about the facehugger? We're not given any reasons. The character's motivation (psychologically relating to something in a similar predicment) is something a human would do, not an AI, which wouldn't have any reason to care. But, sure, let's assume the opposite - so, the droid decides to do the one thing which would guarantee it dies? Why not just coerce it back into frozen stasis?
A human character could have gone down that path. They'd make up the typical David 8-like logic, where the adult Alien would be seen as a 'continuation'/reincarnation of the facehugger. They'd be fearful about self-preservation, but not about sacrificing someone else to that fate. Doing so could even have made a nice call-back to Golic. Or even have the story feature a Newt-alike, who the audience is initially led to believe is a similar distrusting survivor of a massacre, only to be revealed as convincing herself to sacrifice the newcomer for some allegorical 'greater good', before commandeering their ship and leaving the impregnated victim behind, like she's talked herself into believing was a bargain struck with the facehugger (like Golic similarly did).