I have been using mirrorless alongside my DSLR for years now, and they certainly weren't really up to continuous focus in the past - none of them, really, excepting the Nikon 1 series, which took advantage of a much smaller sensor and wider depth of field to help it. I still shot birds, and birds in flight, but always using single focus, and constantly reacquiring.
I upgraded to the Sony A6000 when it debuted, using it with the same lenses as my NEX-5N before it, namely a 55-210mm lens with a max aperture at the long end of F6.3. The only way to get more reasonable reach was by use of a teleextender - I use a 1.7x Sony DH1758 teleextender of an afocal design that screws onto the filter threads, and it gives me 357mm (535mm equivalent in 35mm terms). The good news is that the review above in my experience is exactly true - the mirrorless cameras have caught up to entry DSLRs...if not potentially exceeding them a bit. The A6000 tracks focus every bit as good as my DSLR...and even has some nifty focus features I don't have with the DSLR such as lock-on AF tracking mode, many more selectable focus zones, and much bigger coverage with 179 cross-type PDAF points covering about 90% of the frame. It's superbly fast, no wavering, and tracks beautifully. As for the EVF - hasn't really been an issue for me, as a long-time OVF user. It doesn't quite match an OVF for panning with the very fastest and most erratic birds - following something like a martin or swallow with all its dekes and turns at full speed is already difficult with an OVF, and with an EVF firing a burst of shots, you eventually just can't keep it in the finder. But you can still acquire it just as easily, and pan with it easily when not firing and getting initial focus, and can stay with it through half-a-dozen or a dozen shots before you lose it - so it's not like you're out of the game...you just generally can't keep the bird in the frame for as long and for as many shots.
Absolutely and without doubt, the GH4, A6000, EM1, and XT1 are a step above their mirrorless large-sensor competition and forebears. Having a previous M4:3 or NEX model won't give you even close to an idea how fast the focus is on these new-gen mirrorless cams, and how well they can continuously focus and track the subjects. It's nice that my second body cam, which I bought as a light second body to the DSLR, or to sometimes take its place when it was too hot to lug the big gear around, can now cover for all the same types of shots, lacking only in reach and fast lenses...previously when bringing the mirrorless, I could get the occasional BIF shot, maybe 1 for every 100 still shots...but now, I am shooting roughly 50/50 on BIFs and still birds with the A6000 and the hit rate is dead-heat with the DSLR.