Do S.M.A.R.T. tests wear out the hard disk?

Yes, albeit marginally. Any action that results in mechanical motion is an action that is helping the system die. Hooray for Entropy. That which doesn't kill you only brings you closer to death....

Keep in mind though, the disk is continually accumulating stats, so just glancing at the stats should tell you whether the disk is healthy enough to run the test.

Here is some info on what each level of test involves (footnote references removed): https://en.wikipedia.org/wiki/S.M.A.R.T.#Self-tests

SMART drives may offer a number of self-tests:

Short Checks the electrical and mechanical performance as well as the read performance of the disk. Electrical tests might include a test of buffer RAM, a read/write circuitry test, or a test of the read/write head elements. Mechanical test includes seeking and servo on data tracks. Scans small parts of the drive's surface (area is vendor-specific and there is a time limit on the test). Checks the list of pending sectors that may have read errors, and it usually takes under two minutes.

Long/extended A longer and more thorough version of the short self-test, scanning the entire disk surface with no time limit. This test usually takes several hours, depending on the read/write speed of the drive and its size.

Conveyance Intended as a quick test to identify damage incurred during transporting of the device from the drive manufacturer to the computer manufacturer. Only available on ATA drives, and it usually takes several minutes.

Selective Some drives allow selective self-tests of just a part of the surface. > The self-test logs for SCSI and ATA drives are slightly different. It is possible for the long test to pass even if the short test fails.

The drive's self-test log can contain up to 21 read-only entries. When the log is filled, old entries are removed.

Information on different types of SMART test

Short

Checks the electrical and mechanical performance as well as the read performance of the disk. Electrical tests might include a test of buffer RAM, a read/write circuitry test, or a test of the read/write head elements. Mechanical test includes seeking and servo on data tracks. Scans small parts of the drive's surface (area is vendor-specific and there is a time limit on the test). Checks the list of pending sectors that may have read errors, and it usually takes under two minutes.

Long/extended

A longer and more thorough version of the short self-test, scanning the entire disk surface with no time limit. This test usually takes several hours, depending on the read/write speed of the drive and its size.

Conveyance

Intended as a quick test to identify damage incurred during transporting of the device from the drive manufacturer to the computer manufacturer. Only available on ATA drives, and it usually takes several minutes.

To answer your question, running an extended test periodically won't cause too many undue problems. However, it is putting an wear on parts of the drive for no real reason. I would put the time and effort into a frequent back-up solution, rather than frequent testing of the drive.