This has been tried before but obviously wasn't a huge success. Most combinations used jet power for take-off augmentation and emergency power only.
The airplane used in ConAir (some US military transport) had jet engines (with closeable air intakes) in pylons under the wing and there was a bomber before that as well (B-36?)
A civil airplane using the concept was the Hustler (
http://www.k12.nf.ca/sptech/aviation...ustler500.html) which probably fell victim to the 1980s crisis of general aviation.
As for the merits, there is probably too high a penalty for carrying around useless equipment most of the time, and a jet engine cold-soaked at altitude for several hours might also be hard to start (with heavy wear) as a go-around backup.
There seems to be some merit to the KISS principle and many of the obviously beneficial setups seem not to work in real life.