The short answer is "yes" and I'll explain how.
FamilySearch does not talk to Wikitree directly. Migrating your family tree is doable as a three step process:
1. Install PC software that will act as an intermediary. https://www.ancquest.com/aqbdl.htm
2. Use Ancestral Quest (free!) to export your tree to a file. There are many export types but choose "Other...GED".
3. Upload the GED file now stored on your PC to WikiTree
Ok, now for the messy details:
* In Ancestry Quest (aka "AQ"), select "FamilySearch" in the top menu
* Then select "login" and it will take you to a FS login page.
* Then back to AQ, select "FamilySearch" again and then "Import Family Lines"
* It will ask how many generations and this will create a problem. You want a lot of generations but since WT only imports 5000 people, this might cause some back-and-forth experimentation. 12 generations was too many as was 10 generations, at least for me. 8 generations of ancestors produced a file of less than 5,000 relatives (for me, YMMV).
* It asks if you want to include spouses and children. I said yes although this defaults to "no". With this off, you'll get a narrow-but-tall tree. Turning this on gets you a wider tree with more cousins.
* Let it work for awhile. It took over a half hour on my powerful PC.
Once the AQ stored the GED file on my PC, the upload to WikiTree is doable.