Is there a null HMAC?
It is well defined.
The hash function has no impact on whether HMAC is defined for a null string text argument. As long as HMAC is defined for a particular hash function, the resulting HMAC of a null string text argument should also be well defined.
The definition of HMAC according to FIPS 190-1 is:
$HMAC(K, text) = H((K_0 \oplus opad)|| H((K_0 \oplus ipad) || text))$
If $text$ is the empty string the right hand side simply collapses to
$H((K_0 \oplus opad)|| H(K_0 \oplus ipad))$
which is well defined.
The hash function used has no impact on the existence of the null HMAC.