Yes, but there's a small sacrifice: you won't see the target's name / level anymore.
For the following instructions, you need the latest version of DoTimer. I'm gonna assume that you want cooldowns integrated into your target's debuffs, and that you only want to move specific cooldowns.
In DoTimer, select the anchor you want your target sent to (can be the default location, it doesn't matter). Then, in the 'move targets here' editbox, type "*target*" (no quotes). After hitting enter, open up the dropdown next to the editbox, mouseover "*target*", and in the submenu, select "Use Standard Name". In the "Standard Name" editbox, type "Target" or something.
In Cooldowns, select the anchor you selected from DoTimer. In the "move timers here" editbox, type in all the cooldowns you want moved. After each one, do the same thing as above - dropdown menu, mouseover, submenu, select "Use Standard Name". When done adding, type "Target" or whatever into the "Standard Name" editbox. Note: this must match exactly the one you typed in DoTimer!
In essence, what you are doing is telling DoTimer and Cooldowns that, for these targets and timers, you want to overwrite the timers' default target data with something you select - whatever you typed into the "Standard Name" editbox. The rest of the config was just moving the timers to the correct anchor. DoTimer's timer-managing system merges groups of timers that have the same group information, so the end result is a single group with both your target's timers and your cooldowns.