Sure it is.
You simply have to replace the mp3 in the song folder which you can reach through the menu at File -> Open Song Folder in the editor.
After that you may have to adjust the offset because you changed the mp3 (even if you did the cut on the same mp3, mp3 encoding often causes a shift of offset by 5-10ms).
If you have only 1 timing section right now you can do it through the timing tab after making sure this option is checked:
If you already have multiple timing sections (including green ones) write down your current offset, uncheck the option shown above and find the new offset.
Write the new offset value down and revert back to the old offset.
Then open the timing setup panel (F6), click on one timing section and press Ctrl+A to select all timing sections at once.
After that the left side will change where the cursor is:
Now put in the difference between new offset and old offset (negative numbers are obviously legal too!) and make sure the checkboxes at the bottom for "Snap objects to new timing" and "Adjust bookmarks and audio preview" are checked.
When you're done click the "Move" button and finally confirm your changes by clicking OK.
After that everything should be fine. Please report back if it isn't