I have yet to see an arcade game that really bothers trying to hide the fact that its PC based. The best I've ever seen is replacing some splash screens and hiding the OS startup (usually Linux - Windows is too much of a pain), and even that's uncommon. Most just show EVERYTHING, including the inevitable command prompt window that runs all the startup scripts.
It would be much easier to just show a blank screen until you are ready to show something else. I've worked with a Playstation 2 based arcade platform that did that (no joke - it was literally a PS2 in a box with an IO board) in order to hide the startup graphics and sounds. Of course, it makes troubleshooting the system fun since, unless you bypass that, you have no idea if things are broken or if the system is just "booting" for about the first minute or so.
FWIW, you can hide most BIOS startup screens. The process varies with what motherboard/system you have. Many offer a "splash screen" option, and you can often, through the use of some arcane special tools that might just brick your computer if you use them wrong, make that splash screen be whatever you want, including blank. You can also relatively easily change the startup splash of Windows. Hiding the initial login process ("Windows is applying your personal settings" and such) is a lot harder, but apparently it can be done if you hate yourself enough (and/or really enjoy regedit). From there, you can do whatever.
The "cleanest" PC based arcade bootup I've seen is Pump It Up. They show all the BIOS text, but they have their own bootloader, and they completely hide the OS (which is Linux) startup messages. It also boots to completely playable in about 15-25 seconds, which is none to shabby.