MMA is a sport that requires a ton of functional strength, so it makes sense to train with explosive exercises. The main downside of using these is that it requires a lot of time to learn proper form, which can take away from other aspects of your training. With that in mind, I think that Olympic and power lifts help a lot more than they harm, so it's certainly advisable to do them.

Some of the advantages of using Olympic lifts is that they will assist in neuomuscular conditioning and core strength, which are two of the most important parts of MMA. They are by far the best strength-building exercises.

A good Olympic lifting program should be relatively low volume, with an emphasis on intensity and weight. You should take moderate breaks inbetween each exercise session, as these lifts are extremely taxing on the CNS. It will take some time for your body to adapt to them, so be careful less you overtrain.

Here's a sample Olympic and power lifting program (reps x sets):
Monday: dumbbell snatch 2x5 ; deadlift 5x5 ; bent row 5x5 ; good morning 5x3
Wednesday: hang cleans 3x5 ; barbell lunges 5x3 ; high pulls 2x5 ; shoulder press 5x3
Friday: full squat 5x5 ; high swing 5x5 ; upright row 5x3 ; barbell shrugs 5x3

Power training should be done in the 60-70% 1RM range, although you can move higher as you progress. Working in the lower range will help prevent CNS exhaustion, which can result in overtraining as I mentioned above. It's pretty difficult to injure yourself with these exercises, but it's still important to watch your form as your joints can be put in compromising positions.