"Sugar teeth" are teeth damaged by sugar. In that sense it could imply 'having been damaged by something you love and can't get enough of'.
It also reminds me of the expression 'to have a sweet tooth', meaning you like or have a craving for sweet things.
Urban Dictionary's definition of "sugar tooth" is also what you refer to in your post (opposed to "sugar teeth", which you imply), where a craving for something sweet is generalized to a craving for something you can't get enough of, or for something tantalizing.
The meaning of "I'd be sugar teeth" is likely to be found in the overlapping area: 'a desire for something detrimental'.
I'll assume you are referring to this poem, "If I Could, I Would Have Named Myself Honeysuckle", by Robin Gow. In it, the author refers to the intrinsic danger of the beautiful eponymous flower: the presence of ticks as an invisible threat on an otherwise innocent and surrendering entity.
I think the author yearns for that wild, uncontrollable state, simultaneously embodying both the sweet and its detriment.
(I also found this blog post (warning: very explicit content!), where - similarly - "sugar teeth" is a literal combination of 'sugar' and 'teeth', but both in a metaphorical sense: 'sweet, innocent' and 'biting, raw, feral', respectively. This is remarkably similar to my interpretation of the meaning in the poem.)