I can't see any issues with linking the stylesheets with BV (or CV, for that matter) left open during the process. Not on Linux at least.
Unfortunately, my testing seems to have exposed some ugly rendering issues I'm experiencing with Qt5.12.0. It appears to be similar to the recent issue reported on github that manifests immediately after BV/CV loses focus.
With an html tab open in Book View, click on Help->About. After dismissing the resulting About dialog, immediately change to CodeView. Before scrolling or doing anything else: clicking in CodeView to reposition the cursor introduces weird highlighting and missing/doubled lines of text. It's quite atrocious. Scrolling far enough up or down (with either the mousewheel or the vertical scrollbar) seems to remedy the problem.
It doesn't have to be the Help dialog. Any sort of focus activity (like the LinkStylesheets dialog) with BookView open will manifest the issue when first switching to CodeView.
Qt5.12.0 appears to be disaster for Sigil's CodeView.

At least it's not destructive.