Hi there!
Thanks for calling Ann...
The Fireman's Run is "just" another of the dozens of major sports events happening in the city every year, much like the NY Marathon. In fact, we have a number of "races" happening in the city every year... as many as 50! (check the calendar) The vast majority are held on Sunday to minimize inconveniences to other residents of the city. But they don't really affect much, some streets are closed "when the runners are passing" but as soon as they have moved on, so to speak, the streets are reopened to traffic. No event is never allowed to bring the city to a stall... out of respect to the rests of the citizens. To be frank, I wouldn't even have thought about this particular race being problematic or anything, just if you happen to be at the precise moment runners are passing your location.
As per Sant Jordi, this is a very important day here in Catalonia as it's the patron saint of our small nation and it's also the day of the Book and the Rose when thousands of bookshops and flower shops put their stalls in the streets in most towns and cities in Catalonia, including of course Barcelona and also Girona, and people flood the streets in search of a token for the loved ones. The most famous writers come to the stalls and sign books for fans and the whole ambience in the cities is romantic with roses everywhere. Many visitors from all over Europe come on purpose for this sort of celebrations.
But again, it all boils down to your travel style, if you're just looking for museums and stones, then yeah, thousands of people strolling the city can slow you down; if you appreciate traditions then you can't miss this one, but hey, expect crowds... when we celebrate, we do celebrate.
The festivity is celebrated all across Catalonia, but one very special place is in Montblanc, south of Barcelona, where the legend says "Sant Jordi killed the dragon". In this day a medieval fair is hosted in a town that's already in herself a bit of a fairytale town, with the medieval walls, the cobbled narrow streets...
In any case, regardless of traffic or road closures for this or any other reason, or simply when there's gridlock, the metro is always the best option to quickly move across the city. Just sayin'.