I tested it and here's what I got:
Given: level 1 Shakti + 90 gr. Troglodytes without magic take an external dwelling of Red Dragons in the underground with an average loss of 20 Troglodytes.
The minimum stack that 3 Red Dragons are afraid of is 76 gr. Troglodytes.
That is, if there are fewer, the Dragons hit the main stack without being distracted by the single units.
If you use less valuable troops than gr. Troglodytes (e.g., Pikemen) as the fodder (single units), starting from the 2nd round the Dragons hit the main Troglodyte stack without being distracted by the fodder even if there are more than 90 Troglodytes.
If the main stack has 76 Troglodytes and the Dragons get 1 morale, you will most likely not make it out.
If the main stack has 83 (!) Troglodytes and the Dragons get 1 morale, you will make it out no matter what with losses of about 40 Troglodytes.
Troop placement and detailed action sequence are in the presentation file (MS PowerPoint).
In the presentation, comments below the picture describe what happens in each round.
PS The external dwelling of Manticores is not taken any easier, losses are 16-20 Troglodytes!