Yes they can, but I believe that it really depends on which one lops off the victim's head.
I think we see this in the TV series from time to time, but it's hard to remember precisely in which episodes his side-kick is present during a duel.
Also the different movies and the TV series offer different interpretations of how the quickening works or by what mechanism.
I think in the Sci-fi sequel movie, the Quickening was received by whoever was closest in proximity. We see this when Connor regains his immortal status after a train cart beheads one of his immortal attackers.
From the Quickening on Wikipedia:
In the original Highlander film, when an Immortal beheads another Immortal, the survivor is overwhelmed by an invisible force comprizing of a bright flashing light at which point the dead Immortal's body levitates releasing an energy charge in the surrounding area.
JohnP mentions that Ramirez says: "If your head comes away from your neck; it's over."
The Quickenings of this film do not match the other stories. One
Quickening de-ages Connor, who had grown old after winning the Prize.
Highlander 3 (my text):
This one is more like the traditional beheading in the TV series, in that whoever does the beheading gets the Quickening.
This movie represents the only two occasions of a single Immortal
receiving multiple Quickenings at a time....
The fourth Highlander movie follows the television show rather than
the earlier movies...
In the TV series, there is a Watcher splinter cult called the Hunters who presumably execute a number of Immortals, but there is no mention of what happens with the Quickening. So one could guess it just dissipates if the beheading isn't done by an official Immortal.
I believe, for the most part, in the TV series the Quickening is generally received by whoever does the neck-chopping.
The Wikipedia article on Immortals, talks about how "The Game" has the principle of one-on-one combat but that principle is often violated:
Examples of cheating include the group of Immortals who served under
Immortal Jacob Kell in Highlander: Endgame, Slan Quince's modified
sword which fires a dagger from its hilt, and Zachary Blaine
keeping a gun to slow down his adversaries. If the Rules are
interpreted strictly, once two Immortals begin dueling, no outside
interference is permitted, even to save a friend or innocent. For
example, Duncan warns Richie that if he engages the vengeful Annie
Devlin or the relentless Mako in a duel, Duncan will not permit
himself to intervene.