It is unlikely this would cause troop deployments to Ukraine itself, but would likely result in large scale movement of troops to the EU-Belarussian border. But it's not like Ukraine would probably need a ton of help dealing with this, honestly.
Lukashenko is deeply unpopular, his regime only survives because Russia props it up via military force, albeit with only a couple thousand troops actually Belarus atm. As such, Russia does have a lot of leverage.
However, the odds Belarus will actually do this are very low. Mainly because it would be suicide. The Ukraine-Belarus border is heavily defended with mines, fixed defenses, obstacles, natural bariers, and Ukrainian forces with ample drone support. And there are only two highways that cross the border, one in the east north of Chernihiv and one in the west south of Brest. Belarus can't launch a surprise attack, they don't have the men or equipment. And if they were to begin a genuine build up, everyone would see the attack coming and Ukraine's positions would only strengthen.
Both scenarios end one way: the total defeat of Belarusian forces. And with that, almost certainly the collapse of the Belarusian government. And in the event that happens, an anti-Russian government could emerge relatively quickly and seek European assistance or protection. What happens then is anyone's guess, but Russia can't spare the tens of thousands needed to secure Belarus if the current government collapses.
This is a desperation play, but it's unlikely to result in a Belarusian offensive. The alternative could be a large border build up to try and draw Ukrainian forces away from the eastern front. That feels more likely if Lukashenko even does anything, which he probably prefers not to. While Russia keeps him power, it's no secret that he isn't thrilled with the present circumstances.