I'm going to chip in simply to add context, since I live near Barcelona and have done a lot of touring.
The bike can manage the distance, it's a good idea to ask your group how much ground they want to cover every day and over what sort of roads. You can then try to replicate a typical day of riding to their preferences to see if you're going to have problems - bearing in mind that for long distance touring people generally get aches and pains for the first couple of weeks, at 2000 miles you're unlikely to get beyond that stage so you don't want to be at your limit for the duration. There's no shame in just going partway with them and then heading back, or just planning your own shorter tour that you can do at your own pace.
Ask yourself what you want to get from the experience. I remember bumping into a father and son on a pair of Triumph sportbikes on the ferry from France to the UK, me and my partner had covered 1000 miles over 10 days by that point while stopping and enjoying the scenery, food, trying to talk French, and doing activities we couldn't at home. The father and son had covered the same distance in 4 days, mostly on motorways, camping by the side of the road. and eating "cold pasta" because they hadn't stopped for the night until after all the eateries were closed. Neither pair of riders would have enjoyed spending time on the road with the others.
As for Barcelona, parking by the beach might be tricky. What one can do is to ride up the C31 from Sitges to Barcelona (a windy cliff-edge road that unfortunately now has a concrete safety barrier ... nice if you pick a quiet time of day but even if not the views are lovely) and grab a photo near the end from a "mirador" (lookout place) with your bike and the city and ocean in the background. For me personally, I don't enjoy riding the city or anywhere near the coast because the roads are always busy ... inland it's possible to find extremely windy mountain roads that are traffic-free.