I have a Cirrus BXP 5-string, and a genuine Fender hard case (for my Fender bass, not my Cirrus).
The 5-string has a 35" scale length, I don't know what the 4-string has. Lengthwise, it barely fits. If yours is 34", that might not be a problem.
The big problem (which your bass will probably have whatever the scale length) is the angle of the headstock: it's angled back, while Fender headstocks are more or less in line with the neck.. This means the tip of the headstock ends up pressed against the back of the case, and the neck is nowhere near the neck rest. It looks to me like a good way to break the headstock off if the case is handled roughly (which is the point of a hard case, isn't it?).
I have a good quality gig back for my Cirrus, and handle that carefully.