The box will work but if it isn't HD then you won't get HD on your TV - you will get SD either pillarboxed or stretched and it will likely look rather grainy. Some HDTVs have OTA ATSC tuners so they can receive a limited amount of HD channels without any box - see the OTA forum for more details.
BTV's HD STBs will work with all HDTVs. The TV's internal tuner is not used, as mentioned above it's used for OTA (over the air signals via antenna) and does not apply if you're going with BTV. The BTV HD STB plugs into the component video or HDMI ports on the back of the TV. See the following article on the topic: