It won't work at all. EE 2.7 (and most add-ons built for it) use features only available in PHP 5.2+, probably most notable is json_encode
which EE uses a lot internally. Some add-ons such as Store 2 even require PHP 5.3 as minimum now.
Personally I would ditch the host and find one who takes software updates (and therefore server security) more seriously). PHP is up to version 5.5 now and there is no excuse for running software which was released in 2005.