In bridged mode that will certainly drive the cab, but (as many other threads here on Basschat explain) the number of Watts an amp is rated for is actually a very poor way of measuring how "loud" your rig will be.
Although that JB power amp claims 400W, and may even deliver it measurably, how "loud" it will make your bass depends on SO many other factors.
By way of comparison, one of my rigs uses a W-Audio Horizon amp very similar to the one you're looking at, only it's rated 1100W in bridged mode. I play through Barefaced cabs which are (by general agreement) very sensitive, i.e. loud. That 1100W doesn't sound anything like as loud as you might expect from the rating alone, and that amp is simply not as "loud" as when I use my Aguilar Tonehammer 350 which in theory only has one third the output.
If it's at all possible, I'd recommend trying that amp before you buy it. If you have no choice but to buy it unseen, then my advice would be to pass.
If you're anywhere near Acton, you're welcome to come and try my W-Audio and TH350 back to back, to see what I mean.