Hi Ben,
One thing you could do is add a folder connection (right-click on Folders > Add Folder Connection) to your project that contains all of the SDE connection files. For example, if you have all of your SDE geodatabase connections stored under 'Database Connections' in ArcGIS Desktop, you would add the following folder:
C:\Users\<user name>\AppData\Roaming\ESRI\Desktop10.3\ArcCatalog
Note: It doesn't appear that ArcGIS Pro will show hidden folders (i.e. AppData) when adding a folder connection, so you will need to copy/paste the path into the Name dialog box: