Freeview boxes are much more fussy about signal quality (as opposed to signal strength) than analogue recievers. With an analogue TV, less than ideal quality will give you a bit of snow. With a digital picture it can render it completely unwatchable.
If you put a splitter and extra cable runs in, it MIGHT degrade quality enough to give you garbage and very few channels. On the other hand, it might be fine.
The only thing you can really do is give it a try. You might find that your sons freeview box gives a reading of current signal strength and quality just to give you an idea of what your up against.
I have a splitter in the loft. It's fed from th roof aeriel and in-turn feeds one freeview bedroom TV and the downstairs dining room freeview TV. It works fine.
BUT - I used good quality co-ax meant for satellite and cable TV runs, and decent quality connectors. I also researched Freeview boxes and have a relatively good, though cheap one.
The thing to do I reckon, is buy some decent coax and cut over-length. Buy or borrow a splitter, and run the cable down the stairs for now just to see if it works.
If you put a booster in, that will not help quality.
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