Yes we should add the tag.
Using Secespitus' excellent tag creation question for this situation.
1. Ask yourself how many questions you have about this topic: is this probably the only one or is this a topic you want to ask about more regularly?
Only you can answer this, but given that you are asking about it I would say it is likely. I would also think I could ask a few questions on this in the future.
2. Look through the existing questions: how many already use the word or similar words and might profit from the tag?
You've already found 163 questions that talk about it. It is a very common topic and many of those would benefit from the tags existence.
3. Look through the existing tags: is one of them already encompassing what you are trying to convey?
romance is the closest thing we have and we have already identified situations (non-romantic relationships) where it is not appropriate. character-development is close but only deals with a single character not a relationship.
4. Look through Meta: have there been similar requests or precedent cases where something similar has been created/denied?
I can't find anything that relates to this tag.
5. Think about the sites scope: do you think that a lot of people will profit from these tags when they are asking questions about the specific topic of the site you are on?
I can see plenty of scope for this to be beneficial to the site.
6. Think about the tag's scope: is it well-defined and obvious to users coming to the site?
With a decent tag wiki and usage guidance I can't see how this tag would be confusing. "This tag is for questions about creating/developing relationships between characters". Seems obvious to me.
Combining all these things I think that yes we should create this tag. It is useful, well-defined and popular. The only issue will be modifying the romance tag to only be about the genre and moving other relationship related questions onto the new tag.