Not really, because what the blue button does is show you the relative amounts of blue in each colour. Each of the colours has an exactly even amount of blue in them, so looking at them 'through blue' they should look exactly the same shade of grey and black. If you take some out, this isn't possible.
I think the question you're asking is, is the calibration accurate without the blue button? The answer is possibly, but you won't be able to do much better without professional testing equipment or a blue gel sheet - I think Kodak makes one that works well if you just hold it in front of the screen, doing much the same things as the blue button.
Probably best to stop stressing about it, get as close as you can with what you've got and refer to your scopes, so you learn the quirks of your gear.