Not really. Rec 709, for instance, doesn't specify brightness (it does specify response curve, contrast, the absolute coordinates of the colour primaries, and other things).
Part of the problem is that perceived brightness varies massively with display size. Cinema screens, for instance, are often controlled to be at least 16fl. Foot-lamberts are a unit of areal brightness equivalent to 3.43 candela per square metre. Monitors are often specified in nits, which are equal to candela per square metre. Thus the projected cinema image has a brightness of perhaps 55 nits, whereas most CRT monitors produced at least twice that. Many computer monitors are supplied producing 250 to 300 nits, which is five or six times brighter than a cinema screen, but we don't really see it that way.
A lot of people tend toward the idea that monitors should be set up for 100 nits (roughly 30fl), but this is probably a throwback: it's a number achievable by CRTs and it works in a darkened room. Most modern TVs (and computer displays, and cellphone and tablet displays) are much brighter. On a film set the viewing conditions are almost certainly less than ideal and more brightness will be necessary to stop people complaining, let alone achieving any sort of accuracy. It's my subjective opinion that more brightness reduces perceived error due to the surroundings - think of the display "punching through" the contaminating light - but others may disagree.
Quite often as a practical matter it will be necessary to pick a brightness setting on a monitor that the calibration equipment will actually agree to work with. Within that range, pick something that appears subjectively normal and allows you to see all the detail in the image.
Unfortunately, the upshot of all this is that yes, if you're grading for cinema, you really need to go and see it projected.
Oh, and the minimum brightness for the new HDR stuff is 1000 nits. The Dolby Vision grading reference displays go up to 4000 nits. Sunglasses required.