In principle, yes. But I think in practice it would be difficult at best. Pulsars become fainter at higher frequencies, and this dish looks relatively small. So I suspect that combination of factors would mean that there aren't many (if any) pulsars that one could detect with this setup.
> expected rotational frequency of the targeted pulsar and then shifting the phase until the signal is maximized?
A technique like this is one way to search for pulsars. Though you don't use trigger signals since you don't a priori know the pulsar's spin period. So you record data for a period of time, then try many timesteps over which to fold the data and see if there's a pulse at that period. I'm sure there's better ways now, for it to be done.
PRESTO is one of the major pieces of software used to search for pulsars: https://www.cv.nrao.edu/~sransom/presto/