Yes, you can get your lowered Elise on the Eurotunnel. Thousands have for Euro trackdays/Stelvio/Booze runs etc They put you on the lower deck which has no ramps.
Have a nice trip:)
NB: yes, even really low ones*.
* go-on post on the forum just in case, I'm sure plenty of people with agree.
It will be fine, really it will.
Don't forget that your Tesco's clubcard vouchers can be used against trips on the Eurotunnel, but you need to sort this out a good few weeks before hand.