and no, there is no damage in taking the approach you mentioned. in an ideal world you'd be able to rest the 3 days you aren't lifting, but unlike other programs, this one isn't so strict. i frequently find my actual lift days all over the map. i do a beyond 5/3/1 3-day split using triumverate maintenance approach, though.
just listen to your body. the days are set up where compounds shouldn't cause issues.. if you obliterate your shoulders on monday, you have deadlifts next - so should be plenty of time to rest them for chest after that. do not reorder the exercises, they are planned that way for recovery.
AND DO NOT SKIMP ON LEG DAY.
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