I've seen speculation that the pre-IE population of Europe, culturally and linguistically, might have resembled New Guinea - fragmented into little micro-regions (low mobility, long time for dialect divergence). Not a context in which you get a lot of development of immunity. On the other hand, the Yamnaya were pastoralists, which also tends towards low levels of disease; so I'm not sure they would have had the sort of immunity build up that urban populations tend to get by selection. Those populations were in India, the Middle East, and Egypt at that time: are there any traces of plague involved in the Indo-Hittite movement into Asia Minor?

All of which goes to say that although the Yamnaya might have picked up Yersinia pestis from an endemic area -the steppe area is, if I recall correctly, a possible source for plague later on in history - I'm that they would have had a big advantage over the Europeans. I would expect both populations to have had a similar die-off rate.