Without knowing what radar system you are dealing with, I will answer generally.
An AESA relies on an array of normally dipole antennas which are phase adjusted to enhance the gain in a certain direction. In a non-AESA environment, an antenna such as a forward looking radar antenna is normally a dish. The dishes are mechanically articulated to change the focus gain of the antenna to a different spot. Some articulate vertically only, but there are some which can articulate laterally. Additionally, some can alter polarization.
If your radar is a WX radar unit, then normally just the pitch, or elevation is adjustable. Some targeting radars allow lateral articulation which helps scan, identify and track targets both vertically and laterally.
To answer the OP question, if the aircraft is pitched up 20 degrees, and the radar is coupled to the aircraft pitch, then you can expect that the dish would pitch downward. Although, in this example, 20 or 30 degrees is about the limit of most of the radar units I have worked with.
Finally, modern AESA antennas can create multiple beams, which permit active and concentrated energy on selected targets. A non-AESA dish antenna does not really have that capability, although several strategies and methods were used, particularly before the development of aircraft PESA and AESA antennas. A PESA by definition has one lobal pattern, which can be articulated. An AESA may have more than one.