Yes we can. But question is, should it be a part of Pocket Protocol? Or only one of independent applications of Pocket system?

We actually can't do this as part of the protocol, at least not that I know of -- because Steem doesn't "know" about Pocket tokens.

Of course. I did not mean integration with steem wallet. But I can imagine that with some new commands as pocketlistasks, pocketlistbids, pocketbuyoffer, pocketselloffer and some others it can be build on using comments/SBD transfers and confirming bots only. I do not believe it is good idea though. It would be ugly and extreme spamish :-). And for sure it would have a lot of other disadvantages.

But it would be relatively easy - both to build and use :-).

I'm not a coder and can say stupid things...
Bit IIRC Pocket has its own blockchain. Could we place the logic there?

No. Pocket uses Steem blockchain. And a concept of subchain to to be precise.

It's harder than it sounds, at least it's hard to make it really work well. I thought about this a lot, because it would have added a lot of cool functionality. But we'd run into all the same problems that the Counterparty guys did when they tried to do that with BTC/XCP.

To run a real market book, the Pocket protocol would need to be able to control STEEM, which it can't. We could possibly do something much simpler than a market book where I post a personal offer to sell Pocket for STEEM, and the first person to send me STEEM with a particular something in the memo gets the Pocket. But that's just automated one-way escrow, and it has all sorts of its own problems to deal with.

Or another type of bot. A want to sell POCKET for Steem and sends them too a bot with a command in memo:
pocketsend;[email protected],10 STEEM
The bot waits for a transfer of the amount specified in the memo. B make a Steem transfer to the bot with @A as memo, the bot transfers the POCKET tokens to B and STEEM to A, takes a fee if needed. If no transfer has been done after X days, then POCKET tokens are refunded.

A can advertise the offer. The bot can reply to commands and can also have a presence on Discord for listing all available offers.