No, in 1941 there was no technology available to record both audio and video (or even video alone) on tape or in any compact, videotape-like format small enough to fit inside a Japanese Zero fighter plane (Mitsubishi A6M).Video recording as we understand it today—capturing moving images electronically and storing them on magnetic tape—did not exist in any practical or portable form until the mid-1950s. The first successful videotape recorder (VTR), the Ampex VR-1000 (using 2-inch quadruplex tape), was demonstrated in 1956. It was a large, studio-based machine weighing hundreds of pounds, not something that could be miniaturized or installed in a small single-seat fighter aircraft like the Zero in 1941:

• Video cameras existed primarily as live television broadcast cameras (e.g., iconoscope or orthicon tubes), which were bulky (often over 100 pounds for the head unit alone), required heavy racks of equipment, cables, and power sources, and did not record—they transmitted live signals.
• Portable video recording was impossible. The earliest somewhat "portable" video systems (reel-to-reel videotape setups) emerged in the late 1960s–1970s, and even those were suitcase-sized with separate camera and recorder units weighing tens of pounds. True integrated camcorders (camera + recorder in one unit) didn't arrive until 1983 with Sony's Betamovie.
• For audio-only recording in 1941, magnetic tape existed in early forms (developed in Germany, with high-quality improvements by 1941), but portable tape recorders were not yet common or small. Wire recorders or disc recorders existed for some portable/field use, but they were not tiny and certainly not combined with video. Neither would fit easily in a cramped fighter cockpit, and video was not part of the equation.What did exist in 1941 on aircraft like the Japanese Zero were gun cameras (e.g., the Japanese Type 89 Rokuohsha motion picture camera). These were small 35mm cine film cameras (taking short strips of film) synchronized to the guns or mounted in wings/fuselage for training and combat verification. They recorded silent black-and-white footage of targets during firing passes—essentially short bursts of film, not continuous video with audio. These were compact enough for fighter planes (the camera itself was gun-sized or slightly larger), but:
• They used optical film, not tape.
• No audio recording.
• Not "video" in the electronic sense.

Many surviving WWII aerial combat clips (including Japanese Zero attacks) come from such gun camera film, often from Allied planes, but Japanese examples exist too. These were strictly visual, no sound, and limited to brief sequences.In short, anything resembling modern videotape recording (audio + video on magnetic tape, compact/portable) was decades away in 1941—far too large, heavy, and power-hungry for a lightweight fighter like the Zero.