You can import caldav contacts in thunderbird.
Sync Google contacts with Thunderbird using CardDav.
But I think What you really want is this:
https://help.ubuntu.com/community/SyncEvolution.
You can also use evolution's in-built webdav protocol to add a remote cardav contacts.
Add Carddav contacts in Evolution:
You can use any carddav server.But here for example,we are going to use free online carddav service fruux.com.
Step1:
Create a free account on fruux. Cliack on addressbook, then click on Add new Addressbook
& create a new addressbook, call it Fruux
.

Click on the respective address book. It will show the address book details. Copy the source url
from there.
Step2:
Launch Evolution.
Go to Contacts.
Select "New → Address Book".
Step3:
Select address-book type webdav
.

For "Server → URL"
enter the full URL (of the desired address book),which you have copied in step1
.
It will be something like this:
Fruux:https://dav.fruux.com/addressbooks/a329827487445/b3380-ec73-45f5-a4d5-afb7h4/
(your will be different)
Use the following values:
Username: YUOR FRUUX USER NAME
Password: YOUR FRUUX PASSWORD
Click Apply.
DONE!
Add Carddav contacts in Evolution (using syncevolution):
We are going to sync fruux addressbook with default evolution addressbook Personal.
Craete a fruux addressbook as mentioned above & copy the source url
. Run following commands in terminal-prompt.
Step1:
syncevolution --configure --template webdav syncURL=https://dav.fruux.com:443/ username=YOUR-FRUUX-USERNAME password=YOUR-Fruux-Password target-config@Fruux
Step2:
syncevolution --configure database=https://dav.fruux.com:443/addressbooks/c32487894645/b3fd4500-kc893-45d5-g4d5-afb8645315/ backend=carddav target-config@fruux addressbook
Replace database=" "
with the source-url
you have copied in previous step.
Step3:
syncevolution --configure --template SyncEvolution_Client syncURL=local://@Fruux username= password= Fruux addressbook
Step4:
syncevolution --configure sync=two-way backend=evolution-contacts database=Personal fruux addressbook
Step6 (Run sync for the first time):
Syncevolution --sync=refreh-from-server fruux addressbook
It is recommended to use --sync=slow
or --sync=refresh-from-server
for first time sync option to avoid duplicity.
refresh-from-server
DELETES EVERYTHING in client & REPLACES WITH SERVER (Opposite for caldav/carddav)
Step7 (run normal two-way sync):
syncevolution fruux addressbook.
You can create a launcher with above command to automate the process.