An unpermitted finished basement typically does not count toward the home's official square footage in the MLS or on an appraisal, and yes, you should expect issues down the road.
Appraisers rely on public records and permits when determining a home's square footage. If the basement finish doesn't show up in the permit history, the appraiser has no basis to include it as finished livable space. They may note it as "additional finished area" in the comments, but it won't be added to the above-grade or even below-grade finished square footage in the same way a permitted finish would.
When you sell, the lack of permits creates several problems. The buyer's lender may require a permit search, and unpermitted work can raise red flags during underwriting. The buyer's inspector may flag it. And if the work doesn't meet code, the buyer could ask you to bring it up to code, get retroactive permits, or give a credit to cover the cost of doing so.
Insurance is another concern. If something goes wrong in the basement, a fire, water damage, or an injury, your homeowner's insurance might deny the claim if the space was finished without permits and doesn't meet code.
The best path forward is to check with your local building department about retroactive permits. Some jurisdictions allow you to pull permits after the fact and have the work inspected. If it passes, you're in the clear. If it doesn't, you'll know what needs to be corrected. Either way, you're better off addressing it now than having it blow up a deal when you sell.
If the work wasn't permitted, the county doesn't know it exists, so it is not on the tax roll. More importantly, appraisers generally cannot count unpermitted areas as "Gross Living Area" (GLA). However: It still adds market value. You just have to list the square footage separately (e.g., "2,000 sq ft permitted + 500 sq ft finished basement") so you don't mislead the bank.
We usually dont count it as livable sqft. It can certainly add value and it can be noted that there is additional living space that has not been permitted, just be sure to disclose. If disclosed properly than issues will be minimized.
Usually an appraiser will not recognize unpermitted space as part of the value of your home. You can list it as additional living space when on the market, and will be seen as value added, however may/may not be reflected in the appraisal as dollars added to your value.