Could push ups and pull ups increase punch speed and power for when doing mma?

Some: These exercises will help strengthen your arms and upper back which in turn will increase power. Speed comes from practicing the techniques required. Increasing your core strength will increase your power as well.

Probably not much: Might help with power but not speed. Generally the power in a punch comes from the hip rotation and not the arms (ask a karate or kung fu instructor to explain/demonstrate this - or try punching without rotating your hips!). Speed comes from being relaxed as you initially throw the punch and not tightening your arm until just before impact. If your muscles are tense you can't throw a fast punch!