No. Being able to record video was an evolution in technology and it took a long time to get there.
To understand why you have to first know that video is a sequence of images captured continuously at a steady frame rate and sustained over a relatively long interval.
Since video would not be very useful without seeing what you are filming, Live-View is a prerequisite for video and that feature had to be invented and perfected. The first implementation was B&W and lasted at most 1 minute courtesy of the Fuji Finepix S2 Pro. Olympus made it color with their E-330. It was able to focus thanks to a second sensor in the viewfinder chamber. Later, contrast-detect AF was added.
The implementation of Live-View faced two challenges, one is to get a feed at 24 FPS to keep the display updated and the other is to make sure the sensor does not overheat while doing that. A lot of innovation in electronic-shutters and power consumption was needed to work through those and modern DSLR will still occasionally give the over-heating warning after Live-View or Video is used for too long.
One you have Live-View refreshed at a reasonable frame-rate (24 FPS is the minimum standard rate for video) and sustained for a while (at least a minute to be useful), you have to encode and stream the resulting video to the memory card. You need to make sure all the data paths to the memory card support the bandwidth needed by the video codec. Video codecs are CPU intensive operations, particularly modern ones to work with HD video and require powerful processors.
A few camera attempted to get there before everything was perfected but results were not very useful. The Pentax K20D for example could stream 20 FPS video at somewhere between VGA and 720p resolution but there was NO preview at all, so you were shooting blind.