MASTER CYLINDER

If the lines under the valve are also reversed, then you will still be proportioning the rear brakes. You would just need to top up the little reservoir more often.
But if the lines underneath are such that you are proportioning the front brakes, well that would be bad.And because the calipers are more or less instant on, yes I can imagine a very short pedal travel. To understand why, you have to understand how the M/C works inside. Get the top plumbing reversed, and make sure the plumbing underneath matches it;that is to say that the big reservoir actually operates the front brakes unproportioned. Then it should work normally, try not to limit the rear fluid excessively, rather try to run as much pressure back there,as possible, short of premature lock up.
Those short lines look like copper on my screen, having a reddish hue.I hope they are not copper. They need to be steel, and double flared.A M/C can generate in excess of 2000psi; I have no idea what it takes to burst a copper pipe of that size, but I sure wouldn't want to find out.
On the rear, what's back there; drums or discs