Yes you can pitch straight onto a cake. However, understand that you are over-pitching. Since the cake has almost all the yeast required to ferment the next beer (some will have died), you will get little new yeast. It is the yeast reproduction that creates much of the precursors of the yeast flavors, so your beer will be low in yeast esters. You will also be brewing your beer with mostly old yeast; it may not be measurable, but you might not attenuate as much as you would when using a correct pitch amount.
I believe you will get a better beer if you only use about a quarter of the cake. The yeast are healthy, and it is still a sizable pitch so you will still get a quick start, but I think you will get a lot more benefit from it.
Alright last question as you seem to know your crap. If I don't want to brew that same day can I transfer all of the trub and yeast into a clean growler and just dump it in my fermenter next brew day?
My cakes are always close to 4 pints. After racking the beer off the cake, I swirl up the fermenter (usually don't need to add water, but occasionally do need a little) to get a slurry, then pour the beer into 4 sanitized pint mason jars. Then store in the fridge.
These days I wash the yeast before using, but for a long time I would just straight pitch a pint jar of the slurry for the next brew. My rule was if it was less than a month old, I would straight pitch, over that I would make a starter. Never had a problem; I even broke my rule by straight pitch jars at 3 months old on occasion (I cringe at the thought now, but I didn't have any problems).
I hope this answers some of your questions.
Warning: slurry when stored will create pressure, so you will need to vent any container every few days to release the pressure.