I agree, I think this is best answered by someone who lives in your area. These types of regulations are set locally.
I think it depends on the city/county/state and how they do the permits and then whether they follow up. City, towns and counties have had their tax bases significantly reduced because home values are going down. My assessable value on my home has gone down every year for the past 3, as have my taxes. Because of this their assessor staffing may have been reduced. However, I would be careful on whether you are counting on that fact to assume they WON'T perform a new assessment if you apply for a permit, because doing a renewed assessment on a newly upgraded home may be the way to INCREASE the taxes, and they may not be missing that opportunity. If the work you are doing requires a contractor, they will ALWAYS pull a permit because they have to by our local law.
When I've had big jobs done, like window replacement, new driveway, the contractor always shows up with a permit they stick to the window/door until they are done. However, I will say I have never had a tax assessor come through afterward and look at my entire home. That's not to say they didn't drive by and look at the improvements.
Also, if the work you are doing requires a contractor, and they are touching things that may need "code approval" like electric/gas/plumbing, again, it's possible the person assessing it may notify the town/city/county........or not. But they will have to have a city inspector come through to review the changes to make sure they "meet code" .
When I have purchased a home, or re-financed, the mortgage company insists on an appraisal. But that is for the mortgage company to make sure the value of the home is at least the price being financed. What I can't say is whether the assessment becomes part of any town/city/county paperwork transmittal.
Most cities/towns/counties have their tax assessment information online, at least the information as to how they are computed. May have assessment information and what triggers that. I'd recommend searching the internet or calling the city/town/county offices to get some general information questions answered before you buy.
You state the area you want to move to has high taxes and your home buying in that area has been swayed because of that. Remember, your tax rate is often based on the price of the homes around you, NOT just on your own. Cities/towns stay on top of the re-sale prices of homes in the area, and make blanket assessments based on that and apply them to all the houses in a given tract, subdivision or community. I live in an older suburb, so these reduced re-sale prices during the recent economic downturn is WHY my taxes have been going down. No one has reassessed my own personal home.
Higher property taxes in an area usually mean higher end city/town services, or better schools, or desirable elements in a geographic area. The city/town and county taxes fund improvements as well as ongoing services. If you've been shut out of considering buying a home in an area due to taxes, whether you renovate or not is not necessarily an indication of what you will ultumately pay, the values of the homes in the area will be. Sometimes it makes sense to have the smallest house on a street of mansions, because the PRICE is less........if the city has assessed simply that one home, the taxes may be quite a bit less. But as home prices go up, so will taxes.
Also, mortgage companies will fold in your taxes for an escrow account if you want to go that route. I do. They get the tax bills, based on the city's assessments, then fold that in with my home owner insurance in the escrow account. This has been nice while taxes have been going down, because my escrow account required minimum balance has been getting smaller and in some cases I've received an escrow account refund. Years ago when home prices were going up, my escrow account was short and my monthly payments went up.
Hope that long, involved description helps.