To my understanding: yes, but there are two major problems:

• You'll need a huge number of bacteria to make a difference. Even doing that on Earth will be tricky. What helps of course us that they multiply themselves, but it will take a while nevertheless
• The atmosphere of Mars is very thin due to the absence of a magnetic field. Even if you are able to produce much oxygen, most of it will get ionised by radiation and will be lost eventually

However, the bacteria themselves should be able to survive out there on Mars, if not thrive. They are crazily resilient