Yes, you should definitely try! Before you take the cuttings, make sure you have on hand a very sharp razor knife, rooting hormone, and peat and perlite for the potting soil. Find the youngest, most flexible branches for the cuttings and take a number of them to increase your chances. That will get you started. I know you can find lots of instructions online for rooting cuttings so I won't go into more detail here. I'd also try air layering some branches as I think that might take better. Here's some good instructions for that: https://homeguides.sfgate.com/air-layer-pear-trees-41283.html
. Air layering does take a while but the property may not sell right away anyways.
As far as taking care of the cuttings for their first year, you should be fine as long as they are kept in a sunny location, properly watered and fertilized, and uppotted as needed. You don't want them to outgrow their pots and get rootbound.
One thing I'm not sure of is how much the pear seedlings need to be outside during the winter. Pears do need a winter chill to bud and fruit, but it would probably would be better if they didn't bud and fruit their first year anyways. If they did bud, I would nip the buds off the first year to force the plant to focus on growing both below and above ground. Anyways, I think you'd have to root them in the house so they don't lose their leaves before they've rooted.
Another thing to consider is that the pear trees you want to propagate may well be on grafted root stock. I would try to figure out what kind of pear it is to see it it's root stock is susceptible to any diseases. There are some apps you could download to identify plants and your county extension office could also help. If it is on grafted stock, that may well have affected how big the pear trees grew, meaning that when you grow a pear tree from a cutting, you could end up with a much bigger tree than you expected. That would be another reason to try to figure out what kind of pear it is.