if true; then
echo true
test -e doesntexist
else
echo false
fi
can be rewritten with && and || by making sure the exit code of the code blocks. Instead of
true && { echo true; test -e doesntexist; } || echo false
you need
true && { echo true; test -e doesntexist; true; } || echo false
elif
if test -e exists; then
echo true
elif test -e doesntexist
echo elif
else
echo false
fi
would be
test -e exists && { echo true; true; } ||
{ test -e doesntexist && { echo elif; true; } || echo false; }