Well, yes.
Any antenna requires two parts, whether that is a pair of discrete elements (eg: dipole) or with one provided by "reflection" in a ground plane (eg: monopole.)
This is equally true for both transmitting and receiving antennas since they are reciprocal devices; in general a good Tx antenna will also work equally well for Rx.
However, and this is where it all goes wrong, one does not need a perfect antenna system to get reasonable performance from a radio, whether Tx or Rx or both. Certainly spending some time and effort making sure the antenna is a good as it can be will help with both but you can do OK with something a bit "off" as most HF antennas are.
Generally, VHF/UHF antennas on magmounts use capacitive coupling from the metal base to the vehicle body and are provided a reasonable groundplane by that method; this is why a hamstick on a magmount does not perform well at all...the capacitance is insufficient at the operating frequency to give decent coupling so a poor ground plane results.
Now, to your particular antenna...the type you describe has some metalwork under the feedpoint so will be OKish without a metal groundplane at the top end of the frequency range but below that its performance will drop off. Popping it on a biscuit tin or baking sheet will help quite a bit but you could equally well use a steel window frame, a tin roof on a shed, etc. Popping it on the windowsill may or may not get the performance you want but you can always add some metal underneath it. Note that if you don't need it to stick and stay put (eg: on a vehicle in motion) then you don't need to use ferrous metal the magnet will stick to so a sheet of aluminium foil will work wonders...
