In order to wet the pads and component terminals, yes, the wave has to touch the body of the component. Generally the process subjects the component(s) to a much higher heating rate (when it hits the wave), so you have a higher failure rate than reflow.
You are also more sensitive to absorbed water, so parts are usually baked out before processing. The component size (height primarily) is limited as well due to both wave height and the likelihood of the solder pulling the (adhered) part off the board.
If the pads are placed perpendicularly to the wave (as in your diagram above) you may have to change the pad geometry on them to get an effective meniscus due to body shadowing. Parallel orientation is not as sensitive.
Some manufacturers offer specialized wave machines for this type of process, and you need to contact your fabricator to see if this is something they are comfortable with (and what changes they recommend to improve yield).