It gets clearer if you write out the full response:

Are there any phones in the room?
Yes there is phones in the room.
No there isn't phones in the room.

So, if you answer strictly yes/no to the asker's question, you can now see that replying with "Yes there is..." to an "Are there any..." question is grammatically incorrect. The same goes for "Is there any..." questions; the pluralization in the response should match the pluralization in the question.

However, you can modify your reply if you want to imply something, such as in this case, how many phones can be found:

Are there any phones in the room?
Yes there is [a phone in the room].
Yes there are [several phones in the room].
No there aren't [any phones in the room].