This functionality is available in Cheat Engine where the debugger won't be attached until you set a breakpoint or explicitly ask for the debugger to be attached. I've looked everywhere and couldn't find anything similar for x64dbg. It's very useful when you want to view or modify memory of the process which employs anti-debug measures.
Yes, this is possible. You can replace TitanEngine.dll with https://github.com/mrexodia/StaticEngine and “attach” to a running process.
There is however no way to switch debugging modes and breakpoints etc will simply not work.