There will be a (hopefully) minor penalty to memory bandwidth on the processor due to the graphics chip in your processor sharing the memory bus with your processor.
As an absolute minimum your on-chip graphics will have a framebuffer that it has to constantly "copy" out to your monitor for it to display. Assuming a 1920 * 1080 display running at 60Hz that framebuffer will need an amount of bandwidth.
That bandwidth will be in the ballpark of 325MB/s (1920 * 1080 * 3 (24bit) * 60Hz).
On top of that you use extra bandwidth for
- video decoding, bandwidth factors include
- video resolution
- post processing effects (film grain etc)
- desktop compositing
- anything else the graphics might be doing
When watching video I'd go for a "finger in the air" estimate of about 1GB/s total memory bandwidth used.
Which isn't too bad on a modern system. If you have a modern DDR4 system running in single channel then your memory bandwidth is probably in the ballpark of 16GB/s, in dual channel that gets you 32GB/s.
That's still 1/16th (or 1/32th) of your memory bandwidth though.
With the display to the onboard graphics disconnected I would expect the graphics core to go into a "sleep" mode where it will use next to no bandwidth at all. It will probably have an interrupt set up to monitor the display detect lines.
If you're not doing anything intensive or demanding you probably won't notice the difference. It will have a small penalty in the amount of time taken to copy stuff to your dedicated graphics, but again, probably not noticeable.