I'm a triathlete and to be good at each of the individual sports is to train at each one. There is some spill over with general fitness but they're three individual sports. Being able to run a 15:00 5K isn't going to win a TT and a 50:00 TT 40K isn't going to get you a 15:00 5K.

That said I do triathlon for the multi sport aspect of it although I LOVE riding my bike! Cross training keeps things interesting and using various muscles for a good overall physique.

If you do run and enjoy it, build slowly and get some real running shoes. It is a high impact exercise.