Jez,
yep this is entirely possible and the connection string is literally the same string that you use remotely. as an example, here's the one that i use for a site for my originaltalent database from my local machine:
<connectionStrings>
<remove name="OriginalLocalSqlServer"/>
<add name="OriginalLocalSqlServer" connectionString="Server=sql381.mysite4now.com;Dat abase=originaltalent;uid=accountuserid;pwd=account password;" providerName="System.Data.SqlClient"/>
</connectionStrings>
if i need to use the local installation, i just remove the comment lines on the 1st entry and comment out the 'remote' line.
this works 100% for me but i suppose it will depend on your hosting provider regarding incoming connections etc...
jimi
http://www.originaltalent.com