There are a few different things to consider here.

The first is the 'curs' OpenType Layout feature, which may or may not be supported for individual scripts. It is part of default layout for Arabic, as you note, but I'm not sure whether it is in any European script layout engines. When in doubt, experiment.

The second thing to consider is that 'cursive attachment' is a standard GPOS lookup type, as well as being a specific layout feature, so in theory you can associate a cursive attachment lookup with any feature you like. So, for example, you could experiment with putting cursive attachment lookups in the 'kern' feature, and see if/where that works. Risky, because some layout engines might make assumptions about lookup types, but I would consider that a layout engine bug because the OT spec explicitly states that lookup types should not be assumed.

The final thing to consider is whether you really need cursive attachment in your design. Cursive attachment is necessary when you have both vertical and horizontal offsets to joins; if you have horizontal offsets only, you can get away with kerning connections and will get more reliable support in more places. However, there is a real attraction to using cursive attachment, even for horizontal-only offsets, because -- in theory at least -- it locks the two glyphs together so that the connection will not break if somone applies tracking.

Any chances I get [cursive attachment] to work in Latin text?

I tried this recently (June 2013) in all the browsers I use regularly, on both OS X and Windows. It worked great…in only Firefox.

lookup curs {
lookupflag 0;
pos cursive \a < anchor 21 13> < anchor 413 161>;
pos cursive \t < anchor 2 -24> < anchor 338 217>;
} curs;
and in FireFox:

You may also want to look at Pecita and Cochy's explanation of his technique at pecita.net.

I'm doing something similar using Glyphs for a non-Latin script, and I've given up on generating the OpenType Features file by hand — I'm writing a Python script to do that based on descriptions of all the letters and where they should connect.