Not
exactly what you're asking, but you might consider one of these + headphones:
Boss Micro-BR 4 track
http://www.guitarcenter.com/-i1169092.gcPocket POD
http://www.guitarcenter.com/Line-6-Pocket-POD-Guitar-Multi-Effects-Processor-104391875-i1173933.gcTascam GT-R1
http://www.guitarcenter.com/TASCAM-GT-R1-Portable-Guitar-Bass-Recorder-105125306-i1401677.gchttp://www.guitarcenter.com/TASCAM-DR-1-GT-R1-Accessory-Kit-105020473-i1402140.gcKorg Pandora Mini
http://www.guitarcenter.com/Korg-Pandora...754-i1746466.gcKorg Px4
http://www.guitarcenter.com/Korg-Pandora-PX4D-Guitar-Multi-Effects-Processor-103381554-i1124641.gcKorg Px5
http://www.guitarcenter.com/Korg-Pandora-PX5D-Guitar-Multi-Effects-Processor-104821715-i1387080.gcHere is a visual comparison of (left to right) Tascam, my PX-5 and one of my Px4s to my old Aiwa cassette player:

With the exception of the Tascam, none of the devices I pointed out has decent acoustic recording capacity. What they DO have are features like tuners, metronomes, drum synthesizers, and digital amp & pedal modeling.
So with decent headphones, you can rock out like you were playing Texas Stadium. And yes, they are all about the size of an old Walkman.
The ones I own: the Tascam has the external mics, a phrase trainer (loop & slow down stuff for practicing), and takes SD cards. Both it and the PX5 can connect directly to your computer via a USB port. The PX4 is discontinued, but it can still be easily found. It is less powerful than the PX5, but, oddly, the PX5 does not have a belt/strap hook.
The ones I don't own: The Line6 PocketPOD is, I believe, the most popular device like this; the Boss might be the most powerful (and priciest); the Pandora Mini is the smallest (its about the size of a stack of business cards), cheapest, and least powerful.
So, in your case, the strongest candidates would be the Korg Px5, the Boss, the Tascam, or POD. And yes, you can use one like a standard MFX pedal hooked up to an amp...or, s stated, your computer.
_________________________
Sturgeon's 2nd Law, a.k.a. Sturgeon's Revelation: “Ninety percent of everything is crap”.
My FLMS- Murphy's Music in Irving, Tx
http://murphysmusictx.com/