How can I split a shell command over multiple lines when using an IF statement?

The line-continuation will fail if you have whitespace (spaces or tab characters¹) after the backslash and before the newline. With no such whitespace, your example works fine for me:

$ cat test.sh
if ! fab --fabfile=.deploy/fabfile.py \
   --forward-agent \
   --disable-known-hosts deploy:$target; then
     echo failed
else
     echo succeeded
fi

$ alias fab=true; . ./test.sh
succeeded
$ alias fab=false; . ./test.sh
failed

Some detail promoted from the comments: the line-continuation backslash in the shell is not really a special case; it is simply an instance of the general rule that a backslash "quotes" the immediately-following character, preventing any special treatment it would normally be subject to. In this case, the next character is a newline, and the special treatment being prevented is terminating the command. Normally, a quoted character winds up included literally in the command; a backslashed newline is instead deleted entirely. But otherwise, the mechanism is the same. Most importantly, the backslash only quotes the immediately-following character; if that character is a space or tab, you just get a literal space or tab; the backslash will have no effect on a subsequent newline.

¹ or carriage returns, for that matter, as Czechnology points out. The POSIX shell does not get along with Windows-formatted text files, not even in WSL. Or Cygwin, but at least their Bash port has added an igncr option that you can set -o to make it carriage-return-tolerant.

For Windows/WSL/Cygwin etc users:

Make sure that your line endings are standard Unix line feeds, i.e. \n (LF) only.

Using Windows line endings \r\n (CRLF) line endings will break the command line break.

---

This is because having \ at the end of a line with Windows line ending translates to \ \r \n.
As Mark correctly explains above:

The line-continuation will fail if you have whitespace after the backslash and before the newline.

This includes not just space () or tabs (\t) but also the carriage return (\r).