Yes
Lightsabers have occasionally explicitly been described as having a cauterizing effect. For example, when Anakin beheads Dooku, the novelization describes the wound as "cauterized" (of course, the movie supports this, since we don’t see any fountain of blood):
The severed head’s stare was fixed on something beyond living sight.
The desperate plea frozen in place on its lips echoed silence. The
headless torso collapsed with a slowly fading sigh from the cauterized
gape of its trachea, folding forward at the waist as though making
obeisance before the power that had ripped away its life.
Revenge of the Sith (novelization)
Even when the word “cauterized” is not used, the films generally show things this way, as well as not showing any blood.
Anakin’s legs glowing after Obi-Wan amputates them:
The books also almost invariably show severed body parts as exhibiting some degree of burning (if it’s mentioned at all).
He was looking at a hand. The hand had brown skin. The hand held a
lightsaber. The hand had a charred oval of tissue where it should have
been attached to an arm.
Revenge of the Sith (novelization)
And wounds are often explicitly described as having no blood:
“This is what happens to those who would resist the Empire,” the gray
creature said.
He threw his still-spinning lightsaber at Kolvin and sliced him in
half. Kaeden screamed, expecting fountains of blood, but both halves
of the body thudded cleanly to the ground and did not so much as
twitch.
Ahsoka
It’s perhaps worth noting that the new novelization of A New Hope describes Ponda’s arm as "sizzling" after being cut off, so there’s definitely still heat at work:
Han could have sworn the severed arm—not to mention the creature’s
remaining stump—was still sizzling when the old fossil calmly switched
his blue laser sword off.
The Princess, the Scoundrel, and the Farm Boy
On the other hand, it’s difficult to argue with the film. Even in new and improved versions of A New Hope, the arm is definitely bleeding.
So Ponda’s arm definitely was not cauterized. As to why, there are lots of potential explanations, though I’m not aware of any canon one (yet). Most likely, Aqualish have a bizarre physiology, which means that their blood doesn’t boil or coagulate until temperatures are much higher than for humans (or at all). Weirder things have been seen in Star Wars.