You're up early this AM. I'm a life long NYC area resident (30 yrs. in lower Westchester) and a recently retired realtor, so my expert advice as follows:
Yes property taxes can be grieved, but as you noted there is no guarantee. However, in reality, the majority of owners do win their grievances so the odds are in your favor. That said, several towns had assessments in recent years so property taxes did go up (Scarsdale, Greenburgh, Mamaroneck / Larchmont). It's possible more towns will do assessments but who knows? I know the taxes are ridiculous but then it is paying for quality education. Unfortunately school districts have mandated expenses they are required to pay for whether there is money to pay for it or not (Federal / state programs, retired teacher pensions, maintenance). Finally, residents vote on school budgets every year and they pass with tax increases, so be prepared for this even if you win a tax grievance.
As for this foreclosed house, if it's located in one of the following SCHOOL DISTRICTS (Pelham, Larchmont, Rye, Harrison, Scarsdale, Bronxville, Tuckahoe, Irvington or Ardsley), I would definitely buy it no matter how much the taxes are and do whatever it takes to get that house. If this house is located in these school districts (New Rochelle (10801 - 10805), Eastchester, Hartsdale, White Plains, Tarrytown or Dobbs Ferry), I would not be so eager to buy this house. Although the school districts are good in all of these towns, they don't rank as high as the ones mentioned before - Pelham, Larchmont, etc. The other issue is home values are not as high as the other towns either, so if you spend money renovating this foreclosed house, you need to question how much of a return on investment will you get when it's time to sell. A foreclosed home after renovations in New Rochelle (10804 for example) will not get the same selling price as a nearby home in the Scarsdale school district even though they are 1/8 mile apart. If this home is located in Yonkers, Mount Vernon, Greenburgh or Port Chester, don't buy it and move on - unless you get it for real cheap.
What you need to do - VERIFY the school district! Don't believe anything your realtor tells you. You need to contact the school district itself and verify this address is within that school district's attendance boundaries. There are too many houses especially in the Scarsdale area where the physical address is Scarsdale 10583 BUT the school district for that house is either Yonkers or New Rochelle, etc. - NOT Scarsdale. Same applies for Rye, Rye Brook & Mamaroneck. Also White Plains, West Harrison & Harrison. It makes a HUGE difference in the value of the house. Bottom line - realtors will not do this for you. Also on every listing it states in tiny print at the bottom of the listing - "The information provided herein is NOT guaranteed but is to the best knowledge of the provider. The buyer is responsible for verification."
As for you bidding $100K less, I would not go that low. If this house is in Pelham, Larchmont, Scarsdale, etc., the bank / seller will give you the middle finger & curse you out. Start with $50 - 75K less and tell your realtor to have an escalation clause so you can increase your bid if you get rejected.
Good Luck! Any further questions, feel free to ask.