The short answer is, yes, the pressure will most probably build to a point that the hoses and/or connections will fail with the system blocked downstream of a simple flow restricting orifice.

Most regulators for aviation use (i.e. Mountain High E & S) have an internal diaphragm that shuts off flow when the downstream pressure equals the upstream pressure. I highly recommend regulators with this feature, for obvious reasons.

At the same time, I can also recognize the (cheaper) alternatives IF YOU DO NOT SHUT OFF THE FLOW COMPLETELY. The pressure will not increase to the point that mechanical components (tubes and connectors) are likely to fail. However, don't forget to turn the flow rate up when you salvage your flight with a low save and are feeling like a superhero for getting back above 12,000. I have heard more than one badly performed bit of karaoke on the radio when somebody forgot to adjust the O2 flow at altitude.

Pressure in the cylinder is often at 2,200 psi or more (using Aviators Breathing Oxygen from a reputable supplier) but nominal pressure is generally from 1,800 to 2,000 psi on a full tank. Most regulators (orifice type) only reduce the pressure to 15-100 psi, and do not shut the flow off when this pressure is reached, allowing the downstream pressure to eventually try to match the much higher cylinder pressure, resulting in failure of the downstream components. Don't worry, your head won't explode, but you might freak out at the sudden pop and hissing noise when it happens. And then the cylinder empties at an enthusiastic rate.

Please extinguish your cigarettes when this happens, or your whole airplane might explode. or at least turn into a merry little fireball.

Regulators with a diaphragm will regulate the pressure to the optimum level needed to operate the delivery mechanism, whether it is an electronic demand system (MH EDS) or a simple flow meter. Medical regulators are not capable of doing anything but reducing pressure to a manageable rate suitable for a constant flow rate with no change in altitude (and therefore increased O2 requirement).

In a nutshell- buy the best stuff for the application (aviation). If you get cheap crap because you are, well, cheap, don't shut off the flow entirely..

It is just your life, so go as cheap as you think it is worth. Remember that Oxygen refills are generally pretty cheap, and unless you have an extremely small cylinder, saving O2 by shutting the flow down doesn't save much in the way of time vs. altitude. Especially when you have to constantly remind yourself to turn it up at altitude or turn it down when the "houses get bigger." The automatic demand systems (M H E&S) take that out of the equation, so you can just concentrate on flying as best you can.

(I have been giving this lecture to hang glider and sailplane pilots since 1988, when I started selling 02 systems. I am also a dealer for M H E&S. In 2014, I got 147 hours of airtime. I was on 02 for 136 of them.)

Have fun, but don't be stupid. Just because you do not use 02 very often does not mean that you should go cheap. Oxygen is fuel for your brain.