Probably not, given that most solder suckers look like the one below, with a channel the plunger rides in, making it impossible to press against a surface:
I was thinking purely of the larger one like that shown in the original video, with the cocking plunger that extends out from the back. We had one of the smaller ones that rode in a channel at work, and I was completely underwhelmed by its performance, so I've never been inclined to use that type.
Many years ago I had a smaller one purchased from Rat Shack (1980ish time frame), called a Soldavac, IIRC. It was the same blue and yellow colors as the Edsyn one, but shorter in length. It had a rocker on the top side to act as the trigger, two hooked finger rests at the front and a hooked cocking lever at the bottom rear of the plunger. That one I held with my index finger over the trigger rocker, middle and ring fingers in the front rests, and would cock it with my thumb, then stabilize it after cocking by pressing the bottom ahead of the cocking lever with my thumb. It was easy to use once you got the hang of holding it, but alas the urethane-ish back cap eventually dried out and crumbled away.
-Pat
ETA image of old solder sucker from 1978 Rat Shack catalog:
ET further add: the image should also show the cocking hook - a hook similar in appearance to the one at the front top area but yellow and protruding from the bottom, facing to the rear, either at the back end or under the rear end of the rocker, depending on whether it's cocked or not. This hook was part of the plunger, and moved back and forth as the unite was used. It also had a longer tip than shown, with a white nose like the Edsyns.