The pop bumper coil wouldn't care. But you'd be doubling the current through the pop bumper relay switch, wiring and fuse and putting extra load on the capacitor and rectifier. An AP-27-1300 pop bumper coil probably has a resistance of about 14 ohms so it's already drawing about 4 amps through the 5 amp fuse.

You could upsize the fuse but then you'd just be kicking the can down to the rectifier and compromising the circuit protection the 5 amp fuse provides. Could you use a weaker, higher resistance solenoid, maybe like one used on a chime or ball gate?

/Mark

What is this coil going to do in the topper? Is it going to be a complete pop bumper assembly or a knocker or a bell?

Your going to make a tommygun fire in the topper arent you?

Better description is paralleling the coils rather than daisy-chain... I'd be tempted to add a separate contact/switch that drives this, either added to the relay or some sort of contact that closes off of the fiber board of of the pop.

Are looking for only one of the Pops to fire it, or all 3?
Adding an additional set of switches to however many Pops
and getting the Hot from a different source would maybe be
the easiest way..

I was thinking along the same lines. Rather than using the DC that the pop bumpers use and relying on the rectifier, you could use AC and rely on the beefier transformer instead. The easiest approach might be to add a switch to the 10pt relay in the backbox so that it fires any time you get 10 points (including all three pop bumpers). A more interesting solution might have it happen only occasionally, like when you hit a 3000 point target. (That would require an extra switch on the 3000 point relay instead.)

To be truthful, if you're going to have it operate every time 10 points are made,
I'd just tap into the 10 Point Relay's hot. I've done similar things a few times.
Recently I converted a Chicago Coin Replay Sun Valley machine into a True 2
Player Add-a-Ball. One thing I did was tie the 200 Point Relay into a Step-Up-Unit's
Coil that I fabricated into a wiper. It pulls it with ease.

Or you could just add sound effects with a little wav player

https://www.amazon.com/Adafruit-Audio-FX-Sound-Board/dp/B00Q3U42DM

Actually, I believe the Score Relays do have open slot(s), but I'm just
interested in knowing. What makes you feel hooking up directly to the
10 Point Relay's hot terminal would be a problem? The Hot's already supplied..

If it did work, it would be easy, quick, and save some time.
The Score Relay takes little pull. What you could first do is
Elegator clip and jump it. I've done this set up quite a few
times.
Weird for this era of a machine, but Balls-a-Poppin had
no bells. It also has no Score Relays, so to add bells, I had to
tap into the Scoring Step Ups, and like all other Coil Relays
I've added to machines, no issues at all.
My last was a Stepper on Sun Valley that is quite spring
loaded, and no problems..
I'm at 100% you would be fine and it would save some time,
but if you prefer a switch, it does have an open slot..

I think what Mopar suggested is to add the new coil in parallel to the 10 point relay coil, although you could just as easily add it in parallel to a chime coil or a score reel coil. But in any event the current through the coils wouldn't be halved since there's no real current limiting other than the transformer capacity. The two coils in parallel would likely see their full current since the resistance through the wires and switches is so low.

Mark and Alberto is right.
On a Ball Bowler, when all 18 Score Reels reset at start up,
they're all running off the same circuitry..

Be cool when you add a little red light in the end of the barrel to simulate a muzzle flash each time your coil is fired.

Green - You could probably put a red 48v panel indicator (pilot light) in there and just wire it directly to your coil. You wouldn't have to run separate 6v wiring or a switch for the lamp that way.
Something like this should work if it isn't too big for your barrel. It's a little over an inch in diameter.
https://www.amazon.com/Pilot-Light-Panel-Indicator-10pcs/dp/B01N68YLSV

Is the coil going to hit a wooden base and sound like a knocker or do you have a different sound in mind?

Also, Is your gun going to be pointed forward as if it was shooting at the player?

If the LED takes, say, 30 mA then the resistor should be 44 V / 0.03 A = 1467 ohms, and it then dissipates 44 V * 0.03 A = 1.32 watts. So you would use a 1.5 k / 2 W resistor - not very big or hot, since the LED is not continuously lit.