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is the laptop powering the display via USB or whatever? Then yes. it will, a bit. or a lot. depends on the monitor.
if it's just a signal and the monitored is powered externally... then not really.
What about VGA, Display Port or HDMI?
I've connected Cintiqs, portable monitors and regular monitors to my laptop. I've never seen a DP or MDP or HDMI screen that didn't also have another power source, but maybe they exist. In any case those didn't seem to affect my battery much, because they were plugged.
I have a portable monitor that connects via usb-c, that one drains the battery but I usually use it with my laptop plugged so I can't really tell what kind of impact it has.
if it's being connected to something like a dock, and full desktop monitor, those monitors have their own power source. mobile displays like this one get power through the usb-c plug.
The links are just for clarity, OP never said what he's connecting them to. since VGA is being mentioned... I assume a full desktop monitor... but, ya know...
Yes, an external desktop monitor plugged to the power.
Then no, it’s power is coming from the wall.
You might see some extra drainage on gpu, unless you’re gaming, it won’t be notable
is it externally powered? it has to get power from somewhere. If the only cable going to the monitor is the DP or HDMI cable, then yes. it's draining the laptop. VGA doesn't carry power- those would be universally externally powered. Though I'm not sure there's any laptops that have VGA outputs still.