Yes this is doable with the following provisos.
You are are the first one to ask me to do it this way.
When I make the BrB appliance I usually make it on a model
of the patient's teeth that they provide or that I make for
them.
That way I can verify the fit of the clear shell (what you
call the "invisalign retainer") upon which I bond the
brackets and tubes and then mount dead-soft wire as thick as
the slots of the brackets I bond on (.018" -020").
I prefer to make it on a current precise model of your
teeth since I believe that that minimizes any warpage
that takes place when the parts are being bonded on.
If I agree to do this for you and the finished piece
does not fit well or does not fit at all you would
accept that proviso.
The usual trays that Invisalign uses to correct the
teeth are somewhat less thick that the material I
usually use to make the BrB.
I believe these retainers may be made of a more durable
(thicker) material.
Is the "invsalign retainer" a Vivera? or a tray that
came from the set you were given to make your teeth
straight?
Or perhaps it is a clear retainer that your
orthodontist made for you in his office as I do for may
patients since it is provide free with the treatment.
Your retainers must go cover the first molars to have
"buccal" tubes.
Proviso: you must realize that the tubes are not
functional in so far as actually being able to resist
the force of a night brace. Consequently, if you intend
to apply a headgear to it will detach the tube.
I do my best to bond the metal parts on so that they are
not easily detached, however, if you do not treat the
BrB like the jewelry it is, you can soon trash it.
The fee is $385.
Cordially, Dr. Ted