It should, as all iPods (excuse the FireWire ones) have a universal dock connection. It's the little rectangular hole on the bottom. As long there the connector on the Logitech fits it, you're good.
Honestly, the dock stereo systems are HUGE ripoffs. The sound quality you get for the price is very poor. You're paying entirely for the docking capabilities. Just get a nice set of computer speakers and a wall charger for the Touch....
Atomheartmother is partially correct. However, there are some advantages to docks mostly unrealized at this point, in that all you can get is stereo sound (and sometimes video) from the 1/8" plug. In the long run, I hope that future docking stations take better advantage of the dock port. Also, many docking stations (unlike a charger and separate speaker systems) provide some stable protection for an iPod.
And there ARE some decent sounding dock stations for the iPod that are priced reasonable (not like the overrated Bose). I just tested the Logitech Pure-Fi Express Plus, which gets an A- from iLounge by the way. The sound was great for the price, the look is retro with a big volume knob, and the price I found it for was $80.
On the other hand, there are some advantages to the separate speaker suggestion. And if you go that route I would like to recommend a nice setup. For the charger, there is the Scosche reviveLITE charger the iPod plugs into the charger, and the charger plugs directly into the wall (no power cord), plus it works as a nite lite and is EnergyStar complaint (about $40). And for powered speakers, I really like the m-audio line of bookshelf speakers. They sound great, quite flexible in usage, and are a great value. The AV 20s list at $80, I have seen them for as low as $60. The AV 40s, are my personal choice, and they add an auxiliary 1/8" plug and a headphone jack on the front of the speaker. I use these with AirPort Expresses to pump sound through the whole house (with an iPod Touch as a remote to AirTunes.)
Why in God's name would you pay $40 for a wall charger? You can get wall chargers on eBay for as little as $3.50 that are undoubtedly the same exact thing minus the night light.
Here's one for $3.50:
http://cgi.ebay.com/WALL-CHARGER-fo...9|66:2|65:12|39:1|240:1318|301:0|293:1|294:50
If you need a brand name, here is a Belkin for $7.50:
http://cgi.ebay.com/Belkin-USB-AC-W...6:2|65:12|39:1|240:1318|301:0|293:1|294:50www
Also, if you're going to be dropping $80+ bucks on speakers, I'd go with a nice 2.1 setup over some studio monitors. You'll get a nice solid subwoofer that way. This one seems to be nice. Though, the one I linked in my original post is a great bang for the buck.
Well, if you had READ my post, I pointed out 4 advantages to the wall charger (not just a night light, which while slightly useful, is secondary to the need), the other three are (1) No Cords, the iPod plugs directly into the charger, (2) security, as the iPod is mounted on this stand next to the wall, not dangling off a cord, and (3) it's EnergyStar rated (which neither of the ones you listed are. Yes, its $40 (although I have found it cheaper) - if someone wants a $10 (or less) wall model then go for it, I only suggested mine. So undoubtably, they are NOT the same thing.
And as for speakers, first the one I recommended could be found for less than $80 (I read reports of $50), second, although I run 5.1 for my home theater (and I am considering 7.2 for the next one), these SOUND amazing without a separate subwoofer (although I don't usually try to blow the doors off when I use them, so if you are looking for pounding bass, your mileage may vary), and they take up less space than a 2.1 system.
Again, go with whatever you like. If sound is important, and security for your ipod is important, the setup I recommended was appropriate. There are hundreds of alternatives out there, though.
The problem with your charger is that you really can't use the iPod while it's charging. So if you plan to have the iPod charging while playing music through the speakers, you might be out of luck. At the very least, it'd be very inconvenient. And forget about using apps or playing games or whatever while it's charging.
And who let's an iPod dangle off of the wall while it's charging. Don't most people set it on the desk while charging? That's like saying that you should plug a laptop directly into the wall rather than with a cord so as to be safe.
Plus, it costs over 10 times as much as the ones on eBay...