A very tricky topic indeed! The cajon drum and a bass drum. To determine if the cajon drum can replace the bass drum is a question that cannot be answered directly. One would need to know what a cajon drum is, and that type of sounds it produces before we can assume that it is a suitable or last resort replacement, or not even a replacement at all. For the purpose of the article, we would assume that you (the reader) do not know anything about the cajon. This approach is to ensure that new users of the instrument and enthusiasts can gain more knowledge about it, even though the question seems like it is asked by someone who has a good knowledge of the instrument, anyways here is a good resources CGuide that will get the beginners started. In short, if you are a pro cajon drummer or a drummer at all, you could use a refresher. Just follow along and follow closely and you would receive a very clear answer to your question.

Relevance of the Cajon Drum to Modern Music
Those who play the cajon know very well what it is able to do, and the varieties of sounds it can produce. It is quite a noteworthy instrument and has proven its importance in the music industry today. The front surface of the box is very versatile in the production in producing bright sounds. It produces a wide range of sounds that one can fuse into any part of the music industry today. Professional drummers knows that the tapa of the drum produces a bright sound, and sounds like a high pitched conga and a very low intensity clap fused together. It is the duality of sound that the cajon drums produces that makes it suitable for the modern music industry since we all know that the clap sound and the conga are integral parts of different parts of the music industry today.
The back of drum has a hole perforated and produces what is quite similar to the sound of a bass drum. The relevance of the bass drum is not restricted to any single part of the music industry but to every other music industry all over the world. Imaging a song without a bass drum sound but uses every other percussion instrument possible. A few songs can pull that feat, but in most cases, you would require a bass drum to enhance the groove of the other percussion drums or sounds. This is the point where cajon portrays its musical versatility, since it is a very dexterous instrument in producing the bass sound. It is why it is believed that the cajon drums can serve as a bass drum in some extreme cases. But we are worried about complete replacement and not last resort replacement. The possibility of this is solely on the quality of the sound production. The cajon drums requires that you attach microphones properly and ensure that the sound is mixed well with a mixer.
The instrument is mostly wood, if not completely made of wood, and the level of bass it produces is dependent on how you position the microphone at the back of the drum and how you produce the sound using the mixer.

Mixing the Cajon Drum Bass Sound
A cajon drum that is properly ‘miked’ would allow you capture all the sounds required to produce the amount of bass needed to resemble the bass drum. One thing you need to know is that capturing all the sounds of the cajon drum would require good quality microphones and an acoustic environment would do a lot of help. The point is that a hard surfaced room or platform would help you better than a padded room if you want more of a boundary effect of the walls on the sound of the drum. The reflective sound is livelier and would produce more bass since your purpose is to replace the bass drum.
After you attach the microphone to box properly, the sounds from the batter head and the rear head are mixed. One of the two microphones would have to be flipped in polarity because the two microphones facing each other on both ends would have negative effects on the sound production. The bass sound might lose a lot of depth in tone, and might not be able to replace the bass drum anymore. An equalizer and mixer come into play here in order to add a boost to the bass of drum. You should also place the microphone closer to the rear hole in order to have a more intense ‘boomy’ sound. A compressor is used here with an attack time of 10 to 20 ms to heighten the strokes on the surfaces.
The bass sound can be made tighter with a Transient Designer or a gate to reduce the level of the boom sounds. You can also reduce the boom sound, if necessary, by adjusting the angle of the microphone to produce the bass sound in a livelier form and would not require much reverb.
Now we can all agree that the only way a cajon drum can sound like a bass drum is if it gets the proper equipment and sound mixing. Without these, all you would here is the sound of a box being struck. It is important, however, to emphasize that no instrument can replace another instrument fully. If it could, there wouldn’t be a need to create it in the first place. So it is safe to say the cajon drum cannot fully replace a bass drum, but can serve as a bass drum in the absence of an actual bass drum.