Sure it could, if you do a lot of pruning and consider only one or few branches. However it would likely not be a very strong engine, because it would miss lots of relevant sidelines/variations.
The "depth" you see in engines does not mean, that the engine calculates all variations to that depth. This would be practically impossible because of the huge number of variations: After just 1 white and 1 black move you already have 20*20=400 different games. With every move that you look ahead this number increases by a factor that is on average around 35.
Because of that, engines are (just like humans) only considering what they think are the relevant lines, by ignoring all other moves. This is called "pruning".
If you do this pruning very heavily you can end up with an engine that can look very deep. However it would look in a very narrow range, considering only one line or so.
It would miss lots of moves/lines and be very weak. Roughly speaking you could say that engines are doing a compromise between depth, width (number of variations) and allocated time in order to optimize for playing strength.