Simple answer is "yes". And as it was said already, you need a half-link to be able to connect the chain again.
The question is - why do you need it for? There are couple of solutions to handle/overcome this issue if your dropouts don't allow it, such as:
- you can acquire a complete "half-link" chain (they are popular among BMX riders) and be able to break the chain at any length
- you can replace the rear cogwheel to the one with one cog more or less (depending on your preferences) to stick to the even number of half-links in your chain
- if the problem is in your dropouts (road-type not allowing for adjustment) you can experiment with the "road-to-pista" dropouts adapters (I know those exist, I don't know how they perform)
The OP has shared some information why the question was asked in the first place.
If I understand correctly, the current derailleur is Tiagra RD-4700 SS, which according to the specs I've found is short cage model:
The OP is asking if switching to Tiagra RD-4700 GS (long cage model, according to what I've found) would be the solution to the problem:
I'd say: yes, using a longer cage model would solve the problem definitely since the longer cage allows for a longer chain (serving the largest chainrings and sprockets) and takes up more slack of the chain (serving the smallest chainrings and sprockets).
I don't own the pictures presented in this post, I've taken them from "the internet" and those particular were found on a ctbike.pl webpage, a bicycle parts retailer I'm not affiliated anyhow, just found them using a well-known search engine.