I have done this sort of migration a couple of times and it is doable but not straightforward. Broadly you have to first get your old site to dump out the content of the field for each entry concerned in a format you can work with (i.e. some kind of structured file) and then create an appropriately capable fluid field and write some SQL to insert this information into your database using the new fluid field definition.
Because the fluid field is relatively new there are no utility add-ons available to make this process easier, and so you have to construct your approach to processing this as a custom exercise.
Whether it is worth the effort depends very much upon how many entries you are seeking to migrate... and how complex each entry is likely to be.
So, in summary, doable but non trivial.