Not really, but it will help. As with all strenuous exercise participants should stretch and warm up before playing. Since typical games require quick sprints followed by a rest having good an-aerobic fitness is beneficial. Players should gauge their play to their level of fitness. All players in poor physical condition or with physically limiting conditions should consult a physician before playing.
Proper footwear is very important.
Some players find that lightweight canvas topped army boots or leather workboots protect feet and ankles in the woods. Other players prefer the support that sneakers give as paintball does involve running. Personal preferences vary, but footwear should not be overlooked. Paint is water soluble and should wash out as normal. Read the rec.sport.paintball newsgroup.