Which screen gets BIOS output during the boot process is up to the graphics card. Some graphics cards output to all displays simultaneously, some will only output to whichever port it considers to be "port 1". Most of the time they're not labeled. In the case of multiple graphics cards, the display goes to whichever one the BIOS detects first. Some BIOSes have a setting that lets you determine if an onboard vs. discrete card should be treated as the "primary".
One thing that you should know about TVs specifically is that most of them do not power on their HDMI port unless the TV is actually set to that input. So if your computer is connected to HDMI2, but the TV is set to HDMI1, the computer may not even see that there is a screen attached at all until you switch the TV over to HDMI2.
Also... some BIOSes do not detect whether or not a screen is attached to the primary display and some do. In the cases where it does, "port 1" might change depending on whether the TV is on or set to the right input. In cases where it doesn't, output may go to the HDMI port whether there's anything connected to it or not, and you may not see anything on either screen.
Unfortunately, GRUB loads very early in the boot process before any drivers. It relies on the BIOS to put its menus up on the screen, so you're totally at the mercy of the hardware at that point.
So short answer to your question is "maybe" :-)
Interesting. My HDMI cable is not actually connected directly to the TV, but rather through an amplifier. If I shut the amp down before I boot, I do indeed get BIOS on my PC monitor. That's still not a solution though... :( – Hubro – 2015-03-30T23:53:42.547
1Ahh. Didn't know about the amplifier. That basically tricks the computer into seeing a display on the HDMI port all the time whether the TV is on or not, as long as the amp has power. Obviously your BIOS is treating the HDMI port as "Port 1", so there is little you can do about it unless the BIOS gives you a choice. Only other option would be to get a cheap discrete video card and see if the BIOS will favor that one first. That has its own set of problems though. I think you might be screwed here. – Wes Sayeed – 2015-03-31T00:06:11.940