i wouldn't do it.... the biogenesis thing has already been mentioned, but you're also tossing in a guy with a potentially high ceiling in yu darvish to get your ryan braun and then two pedestrian pitchers who will significantly downgrade your rotation. you'd go from very likely having pitching as a big strength of your team to having your pitching likely be one of your team's weakest areas
if you wanna try and get braun, try packaging strasburg with someone else (a younger position player with potential?) cuz those pitchers you're getting back should be pretty easily replaceable if your league isn't crazy competitive and you work the waiver wire with due diligence and roll the dice on potentially-breaking-out pitchers and a couple of them stick. trading yu darvish right now as a toss-in in a deal where you're giving up multiple players to get one player and someone else's filler is cutting him short.... i'd hold out to see if yu can start off with an era of around 2.50 after a month or two to see if he's primed to have a run for the cy young in him before i just shuttle him off assuming that he's a toss-in to sweeten the pot in a trade that's basically strasburg for braun.
but hey that's my two cents.... i mean, long-term if you're playing for more than this year and keeping braun going forward it's a better deal because strasburg always will have that big injury concern, and seeing as he's going late 1st / early 2nd in drafts right now i mean how much more value can he have (short of him becoming so good that someone would trade you braun + others for him?)
but yeah, i wouldn't go and cripple your pitching to get braun... i'd get craftier and try to hang on to yu darvish and use other filler if you're convinced that you wanna trade strasburg for braun, especially knowing that there's a potential ~50game suspension looming for him, i'd wanna keep as much strength on my team as i could.
take a look at my thread, would ye!?!? viewtopic.php?f=26&t=456750