I think the odds of a good viewing experience at the Picasso Museum are very low, but March should be better than later in the year, and you never know. You'll probably be over in the Barri Gotic at some point to walk the medieval streets (the tourist office has a good tour that covers part of that area), and the Picasso Museum is within about 10 minutes' walking time from the Palau de la Musica Catalan, the Cathedral and Santa Maria del Mar. You could stop by the museum and take a look (mob scene at the entrance is not a good sign) and perhaps ask what the situation looks like for later that day. You might get lucky.
The Miro Museum on Montjuic is never crowded like the Picasso. You might not encounter a ticket line at all. It's located near the very good MNAC, which draws a good number of visitors but has a relatively spacious facility, so it won't feel crowded. There's a good chance the MNAC won't have much of a ticket line. In addition to the expected paintings and sculptures, the MNAC has a couple of unusual exhibitions I especially like: medieval church frescoes rescued from the Pyrenees and a modernism collection focusing on jewelry, decorative art and furniture.