Maybe. There is no way the EEG system can harm the TMS system, but there are some TMS systems that are essentially useless with some EEG systems. You need a a suitable combination of features in each to be successful at all in using TMS with EEG.
Coils designed specifically for use with EEG will have a cable that exits the coil tangential to the head surface so that the coil does not pass close by EEG electrodes and cables.
A coil to be used with EEG should be passively cooled, since active cooling by means of a fan will induce electromagnetic interference in the EEG.
The TMS recharge mechanism should be designed to avoid inducing electromagnetic artifacts in the EEG.
The TMS system should be shielded so that no more than 3 milligauss of electromagnetic interference from the TMS system’s power supply reaches the electrodes and cables.
The TMS system should be able to produce a TMS pulse in response to an input trigger with a low and predictable latency. Long, but especially unpredictable latency in responding to an input trigger will result in TMS artifacts that are difficult to impossible to remove from the EEG.
Aside from attributes of the TMS system, there are also important considerations regarding the EEG system in this relationship. See the other FAQ entry on that topic.