Here is how your product title gets affected if you edit the title using Google Shopping Feed.
No, when you edit your product title in the Google Shopping Feed app, only your feed title in your Merchant Center gets updated. The titles in your Shopify remains unaltered.
You are given a 150 character limit to optimize your feed title. This implies that you can make your product title more keyword-optimized to serve Shopping Ads well. The more you ad relevant and high search volume keywords, the higher your chances are that your product will perform better.