Captive Aire (and others I presume) have done studies and lab tests pinpointing the ideal location for make-up air to a Type I hood. One of the best methods so far, is with a supply plenum attached to front of the hood. This allows make-up air (usually ~80% of exhaust)to be supplied at the hood, but not directly into it, allowing proper entrainment of the grease/smoke laden vapors rising off of the cooking surfaces.
To answer the original question, no, a short circuit hood is not recommended, and may be interpreted as against code (not 100% sure about that one) Short-circuiting a hood causes inefficient entrainment (the make-up air is supplied too close to the cooking surfaces, causing some of the grease exhaust to billow out of the hood)
In scenarios where a supply plenum is not provided, make-up air may be supplied close to the hood via perforated diffusers, or other supply devices that do not confer a directional flow to the make-up air, other than straight down.
In all cases, tempered (heated) make-up air is required. Some people still try to get away with just using an evap. cooler to supply mua, codes are more restrictive now.