generally newer versions of sql server can restore backups made in older versions. However it is not always possible to restore a backup created on a newer version to an older version of sql server.
that is, a backup made in sql server 2008 you should be able to restore on sql 2012 with no problem
but a backup made on sql server 2012 I'm not sure if you could restore it on a sql 2008 server.
You could create a backup from your host and try to restore it on the local machine to find out if it is possible. If it is possible then there is no big reason to upgrade your local machine. But if restoring the backup fails on the local machine then it might be good to upgrade if you want to be able to run an up to date testing copy of your site on your local machine
Hope that helps,