Well? Would you?
Did it go down the wrong way when I swallowed it?
What you do with your monsters is your own business.
My parents refused to fork out good money for substandard pasta in the shape of animals or monsters. Had to settle for Beef-a-Roni, which in retrospect still seems pretty sketchy.
One would not get hiccups.
One would, however, get stabbed.
Eventually you get used to anything, including monsters, and you have to find something else to scare you. Like forgetting that you had a vital test coming up, or an IRS audit, or something.
Wouldn’t that depend? Zombies are just not that scary. TV proves that, although they cannot be stopped by chain link fences, wearing a thick leather coat provides ample protection. OTOH, vampires are probably good at keeping things fresh. 
Funny enough, I haven’t had the hiccups since I was a preteen. I studied Shotokan Karate as a little kid and they trained us to flex our stomach muscles over and over. Ever since then, if I feel like I’m going to get the hiccups, I flex my stomach sort of like when you force out a belch and they go away.
I swear I’m not making that up. It’s like I have the backstory of Iron Fist except instead of a mystical realm I was trained in a tiny studio in Kitsap County, Washington. And the only superpower I got was really lame.
If you get hiccups and the monster doesn’t help I say unload him. He’s not worth his salt.
An embarrassment to his varied(?) species.
This guy could hire out as a hiccup-stopper.
You could certainly GET hiccups. Monsters (and other scary things) help get RID of the hiccups. They are not a preventative. So you’d get them, but you wouldn’t have them for all that long.
Now I want to adopt a monster (frequent hiccup sufferer here).