You can write anything in cursive. Basically, it looks... Messy :XD Just like any other kind of cursive writing, the strokes are not as defined, some get combined...
Take a look at
this - at the letter in the top left hand corner. That's what Tatsuma's cursive handwriting looks like :) Compare it to this, the Japanese I transcribed off it
In this case it's actually readable, but I've seen cursive Japanese that's really next to impossible to read unless you're used to reading cursive Japanese :sweat (some of the words on the envelope a few pages before the page I linked were not readable)