Yes, Siteground supports SRV domain records. To request them simply open a ticket in the general Domain / DNS issues category in the Help Desk.

Make sure to provide us with the full SRV details in BIND compatible format. Here is an example:

_xmpp-server._tcp.mydomain.com. IN SRV 5 0 5269 xmpp-server.l.google.com.
_xmpp-server._tcp.mydomain.com. IN SRV 20 0 5269 xmpp-server1.l.google.com.
_xmpp-server._tcp.mydomain.com. IN SRV 20 0 5269 xmpp-server2.l.google.com.
_xmpp-server._tcp.mydomain.com. IN SRV 20 0 5269 xmpp-server3.l.google.com.
_xmpp-server._tcp.mydomain.com. IN SRV 20 0 5269 xmpp-server4.l.google.com.
_jabber._tcp.mydomain.com. IN SRV 5 0 5269 xmpp-server.l.google.com.
_jabber._tcp.mydomain.com. IN SRV 20 0 5269 xmpp-server1.l.google.com.
_jabber._tcp.mydomain.com. IN SRV 20 0 5269 xmpp-server2.l.google.com.
_jabber._tcp.mydomain.com. IN SRV 20 0 5269 xmpp-server3.l.google.com.
_jabber._tcp.mydomain.com. IN SRV 20 0 5269 xmpp-server4.l.google.com.