No because it's considered a pet. The only one I can think of which does (and only since very recently) is Ice Storm. It still does very nice damage when fully slotted, especially if there are other debuffs around like Freezing Rain.
CoX 50s: <ill/rad> <ice/ice> <fire/kin> <grav/sonic> <ice/storm> <earth/kin> <kin/elec> <cold/psy> <thugs/dark> <fire/dark> <dark/elec> <night widow> <EM/ninj> <mind/icy>
Bonfire gets containment, its a pet. I think Oilslick might but I've never activated it without using a power that would allow containment. If it doesn't damn thats a lot of ticks
"Well, they found my diary today.
They were appropriately appalled
at the discovery of the eight victims
They're now putting it all together.
Women wrapped in silk
with one leg missing
Eight legs, one body, silk,
spider, brilliant!"
Ah, Cynic, you remind me of a build I did on test once I think - contained bonfire and ice storm 
Was beautiful.
Ice Storm is a few levels away now, but all part of the DoT plan
"Well, they found my diary today.
They were appropriately appalled
at the discovery of the eight victims
They're now putting it all together.
Women wrapped in silk
with one leg missing
Eight legs, one body, silk,
spider, brilliant!"
No it doesnt and i too would like to know why not - unless stuff from the secondaries doesnt get containment damage?
Wytch
----
Wytch
Still Mostly Defiant.
The only pet I have from my secondary is Oil Slick and I dont think that gets contgainment but as its bugged to hell and the damage shows as grey I cant really tell
"Well, they found my diary today.
They were appropriately appalled
at the discovery of the eight victims
They're now putting it all together.
Women wrapped in silk
with one leg missing
Eight legs, one body, silk,
spider, brilliant!"
Lightning storm was quite a big disappointment for me. When I got it, I was like "Woohoo, now I can really start pushing out damage". But the damage never seems to go much higher than 50. 
It would really benefit from containment.
Oil Slick doesn't benefit from containment, but it does so much damage anyway I'm not crying too much about it.
I really should do something about this signature.
Yep Lightning Storm could really use Containment. It's not mobile like other pets so generally unless you're fighting an EB or AV or defending something it only gets a bolt or two out.
Didn't know Bonfire does Containment too actually. Slotted up and used with spammed Fire Cages it might be worthwhile. After the i7 knockback changes I dumped it.
...does Lightning Storm get Containment Damage - and if not, why not?
Is it time for the dance of joy yet?