My last 100 watt high pressure sodium lamp started cycling on me and it ended up leaking yesterday.  Could I replace it with a 100w PSMH lamp and use it successfully? Thanks.

Since you are lives in the US, you must use only metal halide lamps that are rated for HPS ballasts.
Regular pulse start MH lamps, requires their own ballast + ignitors.
Here, most MH lamps (Except probe-start MH lamps and several models such as the Osram HQI-BT/D) can be operated on HPS gear.

In the US, some HPS lamps are made as very low arc voltage - 50..60 V in order to make them work on a choke, but the MH are not, they have high arc voltages on the order of 100V..150V

So if your HPS is a normal low voltage US HPS the answer is no

If (for whatever reason) the HPS is high voltage (the type that is normal for us here) you can use Pulse Start MH



Have to mention, i am confused when you write "PSMH". It is still not clear if you are talking about Probe or Pulse

"A label with a PS before the MH (i.e. 17 PSMH) on a MH sticker indicates that the fixture utilizes the newer pulse start technology, which use different lamps than the older probe start technology."
From: https://en.m.wikipedia.org/wiki/NEMA_wattage_label

The 100W HPS is about 60V arc, so you practically can not use anything else there.
I'm not sure about possible MH retrofits for this power level, the available 10V as the OCV is just too low for any MH.

The MH retrofits to work on HPS ballasts do exist, but for the 250W and higher power, but those are higher arc voltage lamps (150V or so).
The 150W S56 is directly compatible with "standard" 150W pulse start MH, maybe only needs higher voltage ignitor.