This is done all the time. I even do something similar in my vehicle where I have separate VHF and UHF antennas connected to my dual band ham radio.
The key is you need a diplexer (or triplexer) - not a simple BNC T connector. A diplexer is basically a set of filters that allow a specific frequency range to pass through them. For example, the one I use for my ham radio is something like 140-170MHz on the VHF side and 400-500MHz on the UHF side. Connect the antennas to their respective ports, and then connect the radio to the common port. A triplexer is the same thing except it has three ports. These devices also work equally well to connect multiple differing-band radios to a multi-band antenna.
There are a couple reasons you don't want to use a T connector. The important one for receive-only purposes is that the lowband antenna and 800MHz are both receiving the exact same signals, but maybe at slightly different times and strengths. Because there is no filtering to separate the signals, you will get some "mixing" because the signals from the two antennas are slightly out of phase, and this can result in attenuation, noise, and other undesirables on the signal.
For your application, something like the Comet CF-416W would work well. It is 1.3-250MHz on one port and 400-1400MHz on the other port.
Jeff