Probably not. The key is the parallel structure built into the verse:
You shall rise before the aged
and show deference to the old...
—Leviticus 19:32a (NJPS)
So the second statement is a parallel to the first. Therefore, whatever it means to "rise", it must be a sign of deference to the old.
The Hebrew word translated rise here is quwm <06965>, which can indeed be translated:
1a2) to arise (hostile sense)
1a3) to arise, become powerful
1a4) to arise, come on the scene
and so on. In addition, it can simply mean the act of standing up. But there's no way to allow any sort of hostile reading since the point of the law is to show respect for those older than ourselves.
It seems that standing was (and still is) a sign of respect. According to John Gill's Exposition of the Entire Bible:
Fagius relates, that according to the tradition of the Hebrews, a young man was obliged to rise up when an ancient man was at the distance of four cubits from him, and to sit down again as soon as he had passed by him, that it might appear it was done in honour of him. And this was not only observed among the Jews, but anciently among Heathens, who reckoned it abominable wickedness, and a capital crime, if a young man did not rise up to an old man, and a boy to a bearded person. Herodotus reports, that the Egyptians agreed in this with the Lacedaemonians, and with them only of the Grecians, that the younger, when they met the elder, gave them the way and turned aside, and when coming towards them rose up out of their seat; and this law was enjoined them by Lycurgus, and which Aelianus commends as of all the most humane.