Check that the weld procedures and qualifications used cover the different grades. Assuming they do, you can weld them. Even in some quite-dissimilar cases, such as carbon steel to stainless steel.
AWS D1.1 Section 3.3 has provisions for base metal/filler metal combinations for prequalified WPSs..and it does permit welding different grades of qualified carbon and low-alloy steels (see table 3.1). If the WPS has to be qualified by testing, then follow advise given by JStephen.
An unrelated comment: From a quality assurance point of view I generally wouldn't allow similar shapes to be supplied in multiple grades, unless of course the design is based on the lowest grade material.
On the East coast, This is common practice to have wide flange shapes of A992 and have connection material (clip angles, gusset plates, stiffeners) of A36. And, as mentioned in other posts, channels are most commonly procured as A36 material due to the difficulty in finding and cost. Yes they are weldable.
