You probably come into residency with more MSK examination time than MD counterparts, but this advantage does not always keep up throughout residency if you don't keep putting work into it. I think it helped some with body mechanics with amputee care, but again in the long run not necessarily helpful.
I have met a fair number of DOs that use OMT in their clinical practice (mostly sports medicine), and it is well-received by patients. There aren't too many residency programs where this is integrated, since most are not DO PM&R programs, so you have to have a drive to keep that up, or find a program where you can have some mentors/attendings help you continue to progress in this.