You can do this, but as noted it depends on your current LAN. I actually just implemented this a few months ago on my setup. Previously, my remote sites using "tunnel all" hair pinned at the Meraki to hit the internet. What I did was added 0.0.0.0/0 to the data center MX, gave the next hop of the core router, then told it to advertise that route to the spoke sites.
What happens is when the data center receives traffic from the spoke sites, it sends all that traffic to the core. The core sees the routes as being internet and then sends it to our egress vrf. It works flawless and we did it for similar reasons.
My basic topology is just like yours, I run the Meraki in the data center as dual-arm. Here is a picture showing the basic before/after.