This procedure or application is done all the time.
Chemical additive pumps (or pH stabilizers, for example) are frequently applied to processes to add or control the composition of the fluids being circulated. This is a common requirement in many industries. However, the discharges of each of the two different types of pumps are not piped directly next to each other. This is done in order to take advantage of the normal turbulance and natural mixing action found in the discharge of a centrifugal device and take advantage of the fact that a check valve is normally installed on the direct discharge of the centrifugal pump, deterring any mixing from migrating upstream.
Normally, the reciprocating pump's discharge is connected sufficiently downstream of the centrifugal pumps such that the pulsations of the former are damped and do not affect the latter's performance. It is the centrifugal that is the most sensitive and a "pussy" compared to the more robust and consistant recip.
There would be reason for concern if the capacities of both types were equal; however this is seldom or never the case. Normally, the recip has a relatively insignificant capacity compared to the centrifugal and the the commingling of the two discharges is unnoticable. As in all process applications, there should be a concern for studying the potential of a hazard or problem in applying the two pumps together. However, on total and detailed review it will be found that there is no reason for safety concerns if the normal safety rules are followed.
As I stated it is the recip, inspite of it's weak flow capacity, that poses a potential hazard in it's positive displacement capability and robust nature. It can, if allowed, create a severe or dangerous over-pressure scenario. However, with an appropriate PSV on it's discharge leading back to the suction source, there should be no problem.
Needless to say, the application should be dealt with at least one Hazop - and an MOC (Management of Change) if this is a process change.