In the majority of cases, no, it does not. It might do more on the progression server depending on haste, weapons, and drum available, but past that, if the bard is using any sensible set of gear, their dual wielding DPS will be superior.
Plus any DPS gain results in a group DPS loss. If they had released another drum that extends the duration of dots and makes the main hand hit harder (like they did in ROF) then it could be questionable (I sometimes have 2 bards in xp groups with a group I play with, the puller/CCer/slower runs dots instead of the group dps songs, the other does the dps songs.)
With the slot3's to extend the tick of the dots, a reasonable combo is to stagger the dots. (I use the examples of the songs, not specifics for the right classes in group but just to illustrate) cast1 warmarch cast2 err...mana song cast3 dot1 cast4 dot2 cast5 warmarch cast6 manasong cast7 dot3 cast8 dot4 20 goto 10 so; /melody 1 2 3 4 1 2 5 6 (song placement) What's this doing? you're getting the 2 core group boost songs as needed, and keeping those 4 dots twisting and getting their full duration. the slot3's give the extra tick, mash A Song Stuck In Your Head and extend everything without having to worry too much about changing setups (which is doable, but in this case, lets keep it simple). So you're still helping the group, and generating nice aggro with those 4 dots, and getting decent damage. But in a group with multiple active toons, you're best still boosting group abilities. Now, equipping a drum over your gear mods? Not really needed. Dual wield and keep those songs running as is. But... This on regular servers or TLP?
I havent tested it but my thinking is that dots plus caster merc is better dps than DW plus healer merc, for moloing. Yea, I know - charm kite. But they shortened the range on that so I dont.