Trouble shooting question. On a solenoid hydraulic valve, like a Red Hat that is just a coil over an enclosed spring loaded valve. If the valve is not able to move freely when the coil is energized, will it cause the coil to draw more power since the valve is not in the normal energized position, causing the coil to work harder to try and close the valve?

If it is DC there won't be any difference at all. The difference between being "air core" and "iron core" (once the slug is pulled in) might make a difference in an AC solenoid.

Some solenoids have two windings, one to pull in which is then interrupted by an integral switch, and a lighter weight winding to hold it in. Otherwise I agree with Greg.