yes, it is possible, it may be raining hard, but if the water runs off the land too fast, then it does not get a chance to soak into the land thus topping up the water table. While it may top up resovoirs, the natural water table is how some water companies determine the state of "Drought".
Actually YES, you can have draught conditions that make the ground really hard.
Then you can have a powerful storm come through and dump a lot of rain on you which cannot soak in to the soil causing flooding.
You never said that, you just asked if it was possible.
It happens a lot in the Southwestern states of the USA. The desert areas have what are called washes and these become large canyons due to excessive water run off.
I blame the Tories.