Only if they want to. Probably they will, because it allows them to deploy more equipment in Belarus and Kaliningrad.
But technically... what those troops are going to do there, outside of messing with the local gene pool? Do they expect to cross the border with Belarus and attack? Or, perhaps, they expect to see Putin's tanks crossing the border in the other direction? None of that is likely. Poland was always fiercely independent, and conquering it is more trouble than it's worth.
Now, Poland is also bordering Ukraine. However deployment of foreign troops in Ukraine is unthinkable because it will be seen by many locals as an occupation. Perhaps the Right Sector and a few fellow travelers will meet them with flowers; but far more will meet them with IEDs (and with EDs that are not I at all.) This will be the final proof that the government in Kiev works for foreign powers. This will start a mass movement to expel "foreign mercenaries," there will be many requests to Putin to help them out, and pretty soon Putin will announce that as a true democratic leader he cannot ignore rightful requests of his Ukrainian brothers and sisters... and so on.
NATO won't be able to win that confrontation because it has no clear reason why they are there, so political support for US soldiers dying in Ukrainian steppes will be extremely low. There will be no legal reason either, as the government in Kiev was never elected - it came to power after a coup, so it has no legitimacy. There will be no military power as well, because NATO has supply lines over half the planet, whereas Ukrainians and Russians have supply depots right there. This is why deployment of troops without any way to use them is only an empty gesture. It not only does not help; it hurts, like flipping the bird to a group of gang members in the street.
A paranoid, insular Russian (and I include the entire Russian leadership in this category) sees things far differently. To them, NATO is an aggressive organization who aim is conquest of Russia. Troops in Poland are at Russia's doorstep, a dagger aimed at the heart of the motherland.