Plants would be likely to absorb nutrition from an unglazed container, but the opposite could also happen...
Clays are colloidal, creating a storage site for nutrition. Clay soils can lock nutrition, so unglazed pots could act in the same fashion. Ancient terra preta often includes pottery shards to help hold nutition in the famously sterile jungle soils. Weak acid respponses from soil biology can etch these nutrients back out from the clay, but their tendency is to absorb and hold nutrient until they are full. Thing is they are not selective and can hold salts just as easily as nutrition (that white grime you see on old clay pots is salts). And if the exchange capacity of the pot is still not full, it could withhold nutrient...
Another good reason not to use ammonia salt fertilizers... Salt build-ups can be phytotoxic (fancy talk for plant killing).
I have seen nursery containers designed just like those collanders and baskets, designed to "root prune" by exposure. Interesting stuff Gnome
Seems I also remember a Floridian guy years back that was creating bonsai simply by stuffing rootballs full of uncut sphagnum; no rock, no pot at all. Worked great for tropicals, especially in high humidity Florida. But no pot at all isn't in our poll either, Victrinia
Plastic is fine for grow out, as Norm suggests. But a mature tree, one truly worthy of the name bonsai (seven years of culture minimally, by Japanese standards) should be in a pot befitting such a tree. Only fine Japanese pots are suited for a truly fine tree, but mica pots from Korea or some of the red and purple clay from China are great for pines and evergreens. It's not so much the location as the quality and suitability of the pot, but the finest pots I see are all Japanese...
The pot is an integral part of a final tree; if you don't have the container already in mind for the finished tree, then selection should be detailed by the quality, the style, and the character of the tree itself. Some rules do apply; I recommend John Naka's words on pot selection...
The selection of pots is another important stimulus that goes hand in hand with the upkeep and improvement of bonsai. It is necessary to know the relationship between tree and pot, as well as the make, type, color, shape, and size of the pot It helps to have an artistic, scientific, and philosphic point of view to obtain the best overall effect. The comparison of a pot and tree is the same for the painting and the frame. One must compliment the the other, not take away from the other."
John Naka, Bonsai Techniques II
Maybe a little deeper than clay or plastic?
Mr. Naka says later
It is not wrong to use wooden boxes, fiberglass, cement, plastic or flagstone for temporary pots, but not permanently.
Naka-san has spoken... Word.