The answer will be probably yes. 23&me test 20% of the mtdna genome and to get your full group it will need the full test.
James Lick’s calculator does a great job with the estimates without all of the relevant positions being tested.
Whether you get you final full sub clade depends on who else in the whole world tests (but with H1c that means mostly USA and Europe). For example I am H4a1a1a with 6 extra mutations. 3 of those are too variable to be used for sub-clade usage but the other three are solid, so eventually I will have 3 extra letters and numbers added, when my matches test. Since all of my ftdna matches are GD=3 i.e. 3 mutations way, then it may be a long wait for me.
When you do get your full results please upload to genbank since that is how the new sub-clades are formed, by the analysis done on our uploads.