Hi hedgesparrow
Sounds as though what you're doing is a bit unconventional, but I've done plenty of things that others thought didn't follow the rules, which turned out well, so I'll be interested to hear how it goes.
Not sure from your e-mail about the timescales involved. Were the planks you bought literally sawn from a tree trunk and immediately taken into the house and used as a table top? Or had the sawmill cut the planks some time ago in which case they might have been semi-air dried when you took them away. The planks will shrink as they dry so if they are screwed to a batten, there is a risk they will split unless the screw holes are slotted in the batten. Most of the shrinkage occurs in the final stages of drying below a moisture content of about 20%, so although the planks may feel dry, the risk of splits and distortion increases with time until dry to suit the ambient humidity, probably between 8 to 10% in your kitchen.
Since the tongues and grooves are already cut, I think it would be advisable to keep the planks fitted together during drying to minimise the distortion between each plank. Otherwise you may find the planks just won't go together because they are all bent differently. I wouldn't glue the joints because the wood will continue to expand and contract. I don't have the exact figures to hand but I would guess a larch table top, 3feet wide, could move between 1/4 to 1/2 inch between summer to winter. It would need very long slotted holes in the table frame to accommodate this amount of movement and a high risk of a joint splitting.
Defects such as surface checking might occur if the planks are dried too quickly, but may not be a problem if a 'rustic' appearance is OK. The risk of serious defects would be much higher with hardwoods, especially oak which is hard to dry to produce high quality timber.
Finish - if the planks end up a bit distorted/rustic, then a subtle finish to seal the wood may be enough rather than a shiney/glossy coating which might look out of place. Many coats of wax would bring out the colour. but it might look good with an oil based varnish/polyurethane thinned 50/50 with turps and applied with a rag rather than a brush. That should soak in to seal the wood and bring out the colour. Main thing is to wipe off the finish after a few minutes rather than building it up in layers, just leave on what has soaked into the wood. Two or three applications should be fine and will look like an oiled finish but won't spoil if a hot cup or plate is sat on it. A pretty indestructible finish in fact which you can polish with wax.
Post some pictures when you're finished.
Andrew