Can you polish a concrete pier block?
Definitely can be polished!

Step 1. Grind the flaking on the bottom with a 3"or 5"diamond cupwheel any grit will work. OR JUST CHIP AWAY WITH HAMMER AND SCREW DRIVER

Step 2. Use polishing grout or rock hard setting powder cement  and fill the porosity in the block with a 6 inch metal spatula. It may take 2 coats and let dry overnight.

Step 3. take a 100 grit polishing puck and with your hand smooth the block out. Once smooth use a lithium silicate densifier. I recommend endurapolish by H&amp;C one gallon about $35. apply 4 -5 coats Since its porous.  Let dry 4 hours or overnight the longer the better but overnight is more than enough. This creates the hard surface that makes it possible to polish. 

Step 4. Polish and Seal, Burnish 
Polish with 400 ,800, and 1500 or even 3000 grit polishing pucks your choice. You may be satisfied with the 400 grit. Either by hand with a single 3" puck or with 5" polishing pad on a variable speed polishing hand grinder. Note if densifier will still absorb add coats between the stages of the polishing phase. Once satisfied with the mirror shine and look apply and Outdoors UV Penetrating Concrete Sealer preferably high shine or we look. Don't over do it just as apply one thin coat with a microfiber pad or rag. Let dry and burnish with a 5 inch 3000 grit burnishing pad on a hand grinder at a high speed at least 3000 rpms. Repeat as needed.