Marrying your stalker is definitely an interesting (and let's be honest: potentially dangerous) life choice.
Before I answer the question, I thought we could look at some signs that your spouse is a stalker:
Spouse follows you without your knowledge or consent (shows up at your workplace, family member's homes, while you're out with friends)
They watch you constantly
They are stalking your social media
Hacking your social accounts to see what you're up to
They call/text constantly
Your spouse always acts like they are rescuing you from social situations
They have toxic or manipulative/gaslighting behaviors
Invades your privacy/does not show respect
As far as your question of "is it possible to have a healthy marriage if I married my stalker?" the answer depends on your spouse. Have they gone through counseling to banish obsessive and toxic behavior? Are they on a path of self-discovery and growth? Do they give you freedom and show you respect? If so, then yes.
If your spouse is still showing signs of being a stalker then you are certainly in for an unhealthy marriage (on that note, I really love this article '6 Tips on how to leave a toxic relationship'. It’s definitely worth the read!) I would encourage you both to seek therapy to get your marriage on the right track!