Yes, it is natural, although be aware that (when referring to searches) the verb "check" implies a relatively brief and cursory look, rather than a deep and time-consuming look. For example:
I checked to see if Google had any good minestrone soup recipes.
This suggests I did a quick search on Google. If I wanted to imply that I spent more time at it, I would use verbs like search, research, or browse, or other more figurative verbs like hunt, scour, explore, etc.
That being said, the time it takes to "check" something is not necessarily brief. It represents the amount of time it would reasonably take to perform the task. For example:
I checked my email to see if she had sent me that photo a few months ago, like she said she did.
Obviously this task might take some time. In this case "check" implies that your search is for a specific item, ignoring anything unrelated. In a similar way, when Customs "checks" your luggage, it might take some time, but it's a cursory search for obvious contraband, not a thorough search to find anything that might be illegal.
Lastly, you can always modify "check" with an adverb to indicate a deeper search:
Customs thoroughly checked my luggage at the border crossing, but they never found the hidden compartment in my computer case.
Because "check" implies something about the duration and thoroughness of the search, it can be a little odd to say "someone checked my things", at least to imply that they did so without your knowledge. If you weren't there, you can't know their intent was just to "check"? It's not wrong, but it does give a somewhat mixed meaning.
Instead I would use a different verb that implies bad intent:
Someone went through my things while I was out of the hotel. I should call hotel security.
or implies a thorough search:
Someone ransacked my room while I was out of the hotel. It makes no sense. I don't carry anything particularly valuable. I wonder what they were looking for?
If the check was with your knowledge, then using "someone" is odd because you know who did it. In that case, it's better to explicitly say:
I know my jealous wife checks my phone to see if I have any illicit texts from young women. Yeah, in my dreams. My life is never that exciting.