Just wondering since I was trying to fast sync Ropsten with Mist and it came to a block number around 600,000 and stopped, so I closed Mist and reopened it and it only got to the "started swarm" part. Then I closed the command prompt and reopened Mist and now it has a ton more blocks and its back to 1%.
I think there are a few questions to be answered here. It seems to me that the OP was syncing Ropsten using Geth from the command line, and also running Mist at the same time.
Kishore's answer assumes the question is asking if, when restarted, Geth will continue to sync in fast mode. As Kishore mentioned, it will. (Still true as of May 2020, at least.)
Another way to look at this is if the client will continue syncing when closed. The short answer is no. There may still be some blocks that the client downloads as it is closing.
I'm including these answers for future visitors to this page who may have interpreted the question in these ways, though a careful reading adds another layer. The OP was syncing Ropsten and started getting stuck around block 600K. This, by the way, is most likely due to the OP reaching the Shanghai attack blocks, meaning that there is a good chance that the client was still syncing, albeit very slowly.
First the OP only closed Mist, presumably keeping Geth running. If my memory serves me right (Mist is deprecated a long time already), Mist would use Geth without activating its client anytime Geth was already running. As such, closing Mist theoretically didn't accomplish anything, and Geth would have continued syncing in the background. This is most likely why there were a 'ton more blocks' when Mist was reopened the second time. The first time Mist got stuck on 'starting Swarm'. I'm assuming this was simply a software error, perhaps due to increased resource consumption during the Shanghai blocks. If this is the case, the OP hadn't needed to close Geth, just restart Mist.
This is of little relevance, though, as Mist is deprecated as a tool, but I figured I should try to set the record straight.