I am slightly remodeling my kitchen (on a slim budget). Because I cannot afford granite countertops, I've decided to use the countertop makeover kits on the Formica that are available and make it LOOK like granite. The kitchen sink that I have can be mounted either under or over, and is currently over. I'd like to have it mounted under. Is that a huge undertaking or even possible? The faucet fixtures are part of the sink itself. I've held off on doing the counter top transformation until I can discern whether the sink can be undermounted.
If the substrate under the formica (which is a thin veneer) is particle board, you must do something about the exposed edge of particleboard around the hole that they originally cut to put the sink into. Not only is it ugly, but it will suck up water and expand and disintegrate.
There are kits to glue a curbing over this edge that purport to waterproof it. I am VERY leery that such a thing can work over the long term. Water just gets in - that's its job.
Your fixtures must be mounted through an apron of the sink that extends to the back? They would remain so, and just extend up from below counter level (there is probably no countertop underneath them now. If you look underneath, you will probably see that the hole for the sink goes back further than the fixtures). This will create a cleaning nightmare :(
The hole will probably need to be neatened up (it's probably not a nice even shape) and it is probably a bit bigger than it needs to be. The sink will be held to the underside of the counter by clips that screw into the countertop from underneath, and you will use silicone on the rim of the sink before lifting it into place to provide a seal (and probably run a fillet around the joint after it's in place, wiping the excess away with your finger).
It sounds like a lot of work, and a lot of things that can go wrong. I'd suggest just keeping it overmount.
The short answer is No
However, you can place an 'under-mount sink' under your laminate top, it just needs to sit atop of your wooded surface. If you plan to laminate the counter yourself, this may be a viable option.
Before you laminate your counter:
Use the pattern included with your sink to (separately) trace out correct size under-mount hole in your counter and laminate material
Cut out both your laminate and counter top material
Place your sink upside down on the top surface of your cut counter top, from below the counter ensure that the sink is in perfect alignment with the hole, then from above trace out the flagged surface of your sink.
Use a router to cut a channel to the same depth of your sink flange thickness.
Seat the sink into the hole, and verify it depth then use an outdoor rated wood sealer / varnish to seal the wood and let it dry.
While the wood is drying you can use an abrasive on the top side of the flange to give your adhesive (you likely want to use an epoxy around the sink edge) a rougher surface to stick to.
Now you are ready to attach your laminate over your counter and 'under-mount-sink' with adhesive.
This video is a good how-to, but recommends using bondo as well