You would need to use Meraki AutoVPN in order for your non-MPLS site to search local ressources at your MPLS sites.
I forgot to mention that! They are using AutoVPN on the non-MPLS sites.
There's a couple of ways in how you can achieve connectivity between your MPLS and non-MPLS sites.
For your MPLS sites, I understand that you are using both WAN interfaces. Then you are probably doing essentially Meraki SDWAN with AutoVPN over both Internet and the MPLS links. With VPN connections between all your MPLS sites. Then you'd just announce subnets from each site and be on your way.
For the non-MPLS site, AutoVPN would create a tunnel to your MPLS sites over the internet, directly as well as whatever internet exit point you have in your MPLS.
There are two main methods.
The first is to use AutoVPN over MPLS. This is the most complicated but by far the most flexible. This is the approach I always try and use first.
https://documentation.meraki.com/MX/Site-to-site_VPN/Configuring_Site-to-site_VPN_over_MPLS
The second is to use AutoVPN for failover for MPLS. As long as the MX is the default gateway at all sites this will also work.
https://documentation.meraki.com/MX/Deployment_Guides/MPLS_Failover_to_Meraki_Auto_VPN
Both of these methods should achieve what you need.
We have a similar setup to you and have removed the complexity by having the MXs at the main data centre in single ended WAN concentrator mode. That was you can have remote sites with two internet connections, two MPLS connections or one of each, it all just works. You will need a separate edge firewall at the main site, but the extra cost is worth the excellent availability in my book.
I did exactly this too.
It is sooo much less complex.