I have been vegan for about 12 years now and have been running regularly for 20+ years. I went straight from omnivore to vegan. It's hard to say exactly how veganism affected my running, as I became much more serious about running a bit before going vegan. I topped out at about 50 mpw prior to going vegan and had a marathon PR of 3:28. Over the course of four years, I was able to bring my weekly mileage up to 110+ mpw and brought my marathon PR down to 2:41.
I have dropped a little weight, but that is more likely due to increased mileage - not diet alone. I don't take any supplements and I don't obsess over protein intake. I donate blood regularly and my iron levels are always well within the desired window. I focus on a real food diet with the occasional junk food (fake meat, sweets, etc.). I cook everything in cast iron pans, eat lots of dark leafy greens, try to include a colorful diet, and generally avoid heavily-processed foods.
This diet was right for me and honestly, if I did see some minor negative side-effects from it - I'd still feel good about my decision. However, I did not see any negatives from my diet change. I understand that not every person will have the same outcome, but if you're curious, I'd say it's worth exploring.