I honestly doubt it makes a terribly huge difference either way, when I'm not paying attention and miss the countdown, I just lead with Haunt, cause casting a "non-free" shadow bolt is lame.
But having your DoTs up for basically the duration of haunt's cast time (1.15 seconds for me) longer, is not even a tic, and it makes it so you have 1 less stack of SE, and no S&F until you reach your filler phase, which is in an ideal situation with my current raid buffed haste (~30%) about 6.4 seconds into the fight.
0: haunt, Corruption
1.15: UA
2.3: BoD (dunno how in your example your UA's cast time+GCD is less than your Corruption's GCD)
4.45: Shadowbolt
6.37+Travel Time: Shadowbolt hits, you gain 5% crit, and 5% damage from SE
8.24+Travel Time: Second Shadowbolt hits, last stack of SE is gained.
Lost Damage: ~10% damage missing from ~2-3 DoT Tics of Corruption,
Lost Damage: ~10% damage missing from 2 DoT Tics of UA
Has all 3 stacks of SE about 8.3 seconds into the fight
0: Shadow Bolt, Haunt Cast
1.15: Corruption
2.3: UA
4.45: BoD
6: Shadowbolt
7.92+Travel Time: Shadowbolt Hits, you gain the last stack of SE
Lost Damage: ~1.15 seconds less of UA, Corruption, and BoD... not even 1 tic of any of them.
Has all 3 stacks of SE by about 8 seconds into the fight
In either situation, any number of different procs could be up at different times (I have Lightweave, Power Torrent, and DMC:Volcano)
Both situations I'd activate Demon Soul and Rune of Zeth before casting my first DoT.
Edit: I have heard before that S&F is the exception to the rule (for debuffs), and doesn't auto-update your DoTs, meaning your BoD if opening with haunt would be missing 5% crit for its entire duration. Haunt does auto-update for DoTs.