I would say that it depends. I know that Dr. House once caught a girl who had a condition where she wanted to get doctor's attention and he did some really bold move with this hunch.
Dr. House moves on his hunch and he (usually?) turns out to be right. Though most of it is focused on the diagnosis of disease.
It's unclear if they cross paths or not and if House is invested in catching Dexter, if House wants Dexter to be caught.
I do feel like though if Dr. House is somehow invested in catching Dexter. He might be able to do that.
A much more interesting question could also be how Patrick Jane from Mentalist could catch Dexter?
I recommend watching this video if this topic interests you (although I haven't watched it myself and I am going to do it just now): How Long Would It Take Patrick Jane To Catch Dexter?: https://www.youtube.com/watch?v=uJB8agSrx-8
I think this was a fun Ask HN and I was actually reading it on the phone and I opened my laptop just to answer it because it caught my attention. I love dexter, its just such a great show in my opinion :-)
Edit: after watching this video I got recommended the video by the same creator about Dr House catching Dexter so highly recommended and this is what the question is about, gonna watch this now.: https://www.youtube.com/watch?v=jaUqLFWn2ng
(Also regarding TV shows, I have to complete last two seasons of mentalist and watch silicon valley as well. I think that I have got a lot of TV shows to watch haha. what are the TV shows that you are currently watching or are intending to do so?)