If the connection to ground is earth ground, and the positive side of the voltage source is connected so there is a potential difference over the resistor, would current flow to ground with a SINGLE (just one connection important!) to ground. This circuit would be considered an "open loop" in the conventional sense. Thanks!
In your example, no. Not continuous current as you know it. This would be like air trying to circulate continuously in a looped pipe with a pump somewhere in the middle...except the pipe is blocked off somewhere along its length. A momentary equalizing charge (we don't really call it current in that context) can flow in the same way air fill flow into an empty tank (or dead-end pipe) and pressurize it. That is what most antennas are. There are multiple increasing layers of complexity and the first one introduced is that "current must flow in a loop". What is often omitted for simplicity is that continuous current must flow in a loop.
The momentary charge would flow until the source and the ground would be considered to be the same potential correct? Where Im going with this is when we connect the chassis of a device to a single ground connection, and lets say a power rail somehow got connected to the chassis, then the current would flow through the chassis to ground without the need for an "closed circuit". Thats what the circuit up there is trying to demonstrate.
Voltage is always measured relative to something else, so prior to connection the positive and negative terminals of the supply will be floating at some offset to your earth, whatever it is. When you connect the + terminal to GND, a momentary equalizing charge will flow to earth (or from earth) to cause the + terminal to be at the same potential as earth. Since the - terminal is always some constant voltage relative to +, it follows accordingly. So in other words, yes you can think of it that way.
Getting shocked by static is something similar. It's the pressure suddenly releasing and equalizing.
If a source you connected this to is AC instead of DC, then this momentary equalizing charge flows back and forth repeatedly trying to equalize the charge in "the dead end" which would be the negative stub of your power supply in this case. This is what most antennas basically are.
It is similar to repeatedly dumping and sucking water into and out of a bucket.
Note that this is contrasted with continuous AC current which also has an oscillatory nature but does flow continuously in a loop. There's no real mechanical-analog for this...unless you think of alternating localized pockets of higher and lower pressure air circulating around inside a pipe loop. But in real life the air pressure distribution would equalize. out inside the pipe loop. I think it would have flow at supersonic speeds so the pressure distributions won't dissipate. Strangely, it begins to feel start to feel similar to electrical transmission lines where you also can no longer ignore the speed of propagation.