I think this would be too broad.
If you search for a common term that may be in multiple tags as well as topics, like
SQL which is present in several dozen tags, do you want the search engine to search the content of all posts for that string, and the content of all posts in tags containing that string as well?
To clarify something, you are saying "search the tags as well", but unless the actual post or title contains the word being searched for, how do we know it's relevant. If a search term is a tag, do you want ALL posts for that tag to show? That's what will happen.
You are already searching the content of every post, so if something gets filtered out that is in what you would consider a relevant tag, it's because it doesn't contain the search term! I think this would be confusing, especially for newer users who don't fully understand the tagging system. I imagine their internal dialogue going something like this:
I searched for dentistry and the top
hit is about electronic toothbrushes?
The second hit is about sensitive
senses? The third hit is about acne? The search on this site is borked, nevermind.