It undoubtably WILL affect the price you'll be able to get but that's mostly up to your buyer. You can ASK whatever you want.
Who graded it D/SI2? If the cloudiness you're seeing is from inclusions and they materially affect the beauty of the stone, that would normally get you to at least I1 and mabye I2 with GIA grading.
Send it, loose, to GIA for grading.
A full report will cost only $105 and you don't need to go through a jeweler or appraiser to send it to GIA.
Call GIA to arrange to ship your stone or walk it into their locations in NY NY or Carlsbad, California.
A GIA report is a much stronger document supporting the grades than ANY appraisal from ANY appraiser.
A GIA report does not assign a value.
Get that from looking at comps online but keep in mind a private person cannot get as much for a diamond as a professional diamond vendor can.
I’m not so sure I would start at GIA. It may not be worth your money. Is it pretty? Have you showed it to some buyers and asked for bids? What did they say both in terms their offers and what they thought the grade was? Bids are generally free and it's easy enough to find out if a dealer will quote you a low price. Ask 'em. It sounds like we’re talking about a stone that will be pretty difficult to sell and if you’re only going to get a couple of hundred or even a thousand dollars at the end, spending $200 and waiting a month to get it lab graded may not be a sound investment ($100 to the lab and $100 for shipping). Having a stone 'certified' as an I2 or even worse an I3 is usually not very helpful as a sales tool. If it really is a D/SI2 then yes, a GIA report saying that would help but this is not a given and your comments above suggest otherwise. Were you the client for this jewelry store appraisal? Did you ask THEM these questions? Helping you to understand their conclusions is part of what you paid them for.
Denverappraiser is giving you the stright scoop on a cloudy diamond. No matter how a visibly cloudy diamond might grade at GIA, you will find the market demand for it very weak. All dealers what problem free stones and strongly avoid any with noticeable detriments. The exact color and clarity will make little difference in finding a willing buyer although if you get a lucky GIA report there is always a glimmer of hope you will find that one buyer who needs the stone you have. The risk versus reward ratio is not good, unfortunately.