Can i let my water dragon and parakeets out at the same time?

we have a chinese water dragon and two parakeets and the both need lots of play time outside their cages of course and i was wondering if it would be possible to train them to be in the same room safe all together. the dragon is still a baby as are the parakeets the dragon aint much smaller than the birds tho but we have the water dragon well trained to do as we want her to but we just got the parakeets so they still need alot of work one bites the female does if shes in distress but the yellow one wont bite only does a soft headbutt.