I like this, but its not exactly the pattern that you will get because the actual ground will influence the pattern and try to push it up a little. Most published patterns are free space and you can/t get that without being very high off the ground or on the side of a mountain with a steep drop off.
The only real concern with hanging most antennas upside down is water getting inside and being trapped around elements inside a radome or in the coax entry or matching components. Very few commercial antennas are rated for this and probably no amateur types.
I have done it. I spec'ed the inverted mounting of a PD201 VHF high band antenna in order to cover a courthouse across the street from the tower site. The base of the antenna was capped with pitch and a small drain hole was drilled in the side of the mount and at the bottom of any hollow components/parts so that any water would evacuate instead of freeze solid and break things over time or infiltrate into the cable.
This performed surprisingly well not only in building, but also within the zone the site was located in. I highly recommend doing this if one needs to contain signal to a given area without sending it out to the horizon, or one is given a coordination to serve a very contained area.
All that said, this is typically not the way amateur radio systems are configured. Most ham systems I know of want to capitalize on "out-to-the-horizon" maximal distance coverage rather than meeting a quality of service within a defined area.
prcguy is right. The main problem you will have is weather. Antennas are designed to be mounted in only one orientation. If you invert the mounting then water WILL get into places you wouldn't expect. As for the radiation pattern, it really won't make much, if any, difference. An omnidirectional, vertically polarized antenna's main lobe will be toward the horizon, if you need a pattern that covers only a restricted area then you use a directional antenna. Cell phone antennas are phased arrays and the antenna itself is usually mounted with a downward tilt. There really won't be any performance advantage to mounting one inverted.