The short & quick answer to yours is "no" b/c those inexpensive T-Mobile prepaid phone is Sim locked exclusively to only work on T-Mo bands, (and does not have 1700/2100 Mhz (3G)4G bands) it will work in some Euro countries but not others since T-Mo has native coverage abroad.

Assuming that you only need voice coverage & don't care for/need SMS/MMS and broadband access - you still want to get an unlocked, quadband GSM phone - with user changeable APN & other network settings accessible - so that you can just pop-in a local Sim card with good rates, activate & just "go"

Here's a GSM coverage map to reference what you will need - http://www.worldtimezone.com/gsm.html

Chances are you can find a good refurbished or even brand new, unused classic "non-smartphone" from a good retail agent in your town (AT&T branded ones tend to be more "universal" than those from T-Mo) for a rock-bottom price, or, goggle it on eBay or local CL's - avoid generic/no-name brands (including those with AT&T or T-Mo only logos) & stick with Motorola, LG, Samsung, Nokia & Sony Ericcson - and you will do fine.

I see the SE W580i, quadband (refurbished) for $30 without contract, even it needs to be unlocked, the added cost for buying the code is as little as $10 via eBay.