Can I just buy shutters and get the same level of protection as new impact windows and doors?
No. A shutter only keeps flying objects from impacting the glass on non impact windows or doors. Your existing non impact window or door still has to withstand the high winds pressure and wind driven rain. 9 times out 10 non impact windows and doors will leak or the opening sash will blow in during high winds due to less rigid frames than impact products) and expose your home to high winds and wind driven rain which accompanies hurricanes.