Timelord.
Yes it can, as referenced by Fallmonk in post#30.
On 21 Sept 1956 a Grumman test pilot Thomas W Attridge Jnr managed to do it in a Grumman Tiger ( Bu no 138620 ). He was flying over Long Island Sound, when, at 20,000ft he fired a 4 second burst from his 4 x 20mm cannon. He maintained heading, selected reheat, and descended to 7000ft before firing a second burst. He was then hit by several spent rounds which shattered the windshield and damaged the engine. He attempted to return to Long Island airfield, but the engine failed on short finals and he crashed in woods short of the runway and was severely injured. He returned to flying 6 months later.
The F14 incident was on 20 June 1973 when another Grumman test pilot, Pete Purvis, was flying with WSO William Sherman from Point Mugu in California. They fired an AIM 7E Sparrow, which pitched up after launch and hit a fuel tank. Both ejected safely.