Are radar bars centered around the horizon or do they move with aircraft pitch?
If i understand your question, you are asking whether the vertical elevation direction of the radar antenna lobe is corrected for when the aircraft is in a pitched up position as compared to a level position. (Whether this correction would be done mechanically in older radars or electronically with AESA radars is secondary)

It probably depends on the particular aircraft and version.
But to my knowledge it is generally not. The antenna will keep its direction within the host aircraft and thus scan a higher altitude volume when the aircraft is pitched up.

Note that the pilot can change the vertical elevation range of the antenna by tilting it up or down manually at any time (if it is not locked on a target) and will probably do so in order to compensate for longer phases of pitch up flight.

As an example, this document is a description of the AN/APG-66 and -68 radar systems of the F-16 Fighting Falcon.
(It is a documentation for a general public simulator game, but you can be confident that it describes the function of the real aircraft very accurately)
See page 11, section "Elevation".
In the case of the F-16, the antenna tilt interface is part of the HOTAS controls, on the throttle:
http://falcon4.wikidot.com/avionics:hotas, see "Antenna Elevation Knob"

When a target is "tracked" or "locked" this is another matter. In that case, the antenna will generally move autonomously in order to keep the target within the center of its detection lobe as long as possible, both vertically and horizontally (azimuth), within what is physically possible taking into account the attitude of the host aircraft versus the target. (See the doc for this also)