I think it makes perfect sense. After a lifetime of being emotionally guarded and closeted, due to a combination of her childhood trauma, compounded by her Vulcan upbringing, and then further by bonding with no one aboard the 
Shenzhou but Georgiou, 
and then losing her too (and through her own actions, as she perceives it) Burnham now feels an inexplicable attraction to "Tyler" that she can't ignore, and is just beginning to allow herself to explore it, not yet realizing that it may be because he is every bit as damaged and conflicted and 
out of place among the others as she has always felt herself to be. She's in for 
yet another trauma, but just 
maybe the relationship will turn out to be one ultimately more healing than further damaging for her, 
and for "Tyler" as well...
-
MMoM