Yes. Here’s what it looks like when one does: if the sore becomes infected, it may have a bad odor and pus may drain from the wound.
Those two signs are part of the usual description of venous ulcers themselves. Infection is part of the expected picture rather than a separate complication.
There is also a fuller list of when to call. Contact your provider if there are any signs of infection, such as redness, increased warmth, or swelling around the wound; more drainage than before or drainage that is yellowish or cloudy; bleeding; odor; fever or chills; increased pain.
Reading those two lists together gives something useful. Odor and pus are the signs of an infected venous ulcer. The longer list is about change — more drainage than before, increased warmth, increased pain. Most of it is comparative, which means the useful thing to have is a sense of how the wound was last week.
Prevention comes first in wound care: always keep the wound clean and bandaged to prevent infection.
There is a complication worth knowing about. Infection can make a wound larger and take longer to heal, and it is one of the factors that prevent wounds from healing. An infection is not only an event; it sets the healing back.
Two of the signs are not on the leg at all. Fever or chills are on the list, and are the ones most likely to be blamed on something else.