On the inside of the Horse Guard fence? No, I wouldn't do it.
On the outside, yes.
Speaking from experience......
You want the electric tape to keep the horses away from the wire mesh. It's just WAY too easy for the back of a shoe to get caught and either there goes the shoe or there goes the shoe, the hoof and the fence.
What is the electric tape attached to? Some sort of posts, right?
I would put the wire mesh on the outside of the posts at the very least. Even better, re-attach your horse guard fencing to fence extenders facing to the inside. (The fence extenders attach to the post.)
The extenders come in two different lengths, 5 inches or 12. Horse Guard sells them as do places like Jeffers. I found Jeffers to have the best price.
The perimeter fence on this farm is sheep wire, the woven wire with the larger squares. Not ideal but what is there. It is on steel t posts with wood posts every so often. We capped the steel posts, put insulators on the wood posts and a strand of Horse Guard on the top of the fence. It has worked well at keeping the horses off the fence and the dogs (big ones anyway) in.
It sounds like your set up will be better so should work fine.
Not exactly what you want to do but I have a 3 board wood perimeter fence with the X's in the center instead of the straight middle board. When we moved in there was NO wire (I could just imagine the things that the horses could get into the spaces of the X). So we put up No Climb on the inside of the fence. I have a strand of the Horseguard on the top to keep the horses away from it. It works just fine but I have to make sure the fence doesnt touch the tape.
In the type of situation and set up you are talking about, I think it would work great. I would put the No Climb on the opposite side of the post that the Horseguard is. There shouldnt be any issues with it touching seeing as the post is sandwiched between.
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