Could be longer to be honest ... but unlikely. Yes DW will release tannins that will give your water a tea-color while also lowering your water's pH. All Perfectly natural and safe for fish ... the pH drop is usually not dramatic.
However a few things you can do to leach out the tannins.
1. Stick the DW in a Dishwasher ... minus soap and dishes naturally .... and run twice on high temp. If your worried about detergent residue, run on empty first, then twice with the DW.
2. Boil the DW for several minutes ... empty, re-boil then rinse. Boiling really helps release tannins. Problem usually is finding a pot large enough.
3. Stick it in a tub, bucket large enough and just leave it for a week or two, every couple of 2-3 days switch out the water.
4. Adding carbon to the filter will help clear up the water.
However please note even with all that ... some DW may leach tannins for months ... even years depending. Honestly ... don't worry about it, PWC's will help clear up the water ... if you really want that piece of DW ... get it. I'm eyeing one at an LFS so I'll probably do the diswasher, then boil ... then into the tank.