Yes...for that ring, it will be visible, but if you cover the whole thing in trunk-liner carpet (instead of paint or vinyl) you would never notice that it was hand cut with a jig saw.
A word of advice...whether you use a router, rotozip, or dremel, always make several passes using the circle jig (2 minimum). The first time you go around you don't want the center to pop out before you are finished. Some people actually recommend routering 3/4 of the board and then using a jig saw for the rest (and allow a sloppy cut by staying along the inside of the channel). Then use a template bit on the router to trim the extra wood off after the piece is removed.
A word of advice...whether you use a router, rotozip, or dremel, always make several passes using the circle jig (2 minimum). The first time you go around you don't want the center to pop out before you are finished. Some people actually recommend routering 3/4 of the board and then using a jig saw for the rest (and allow a sloppy cut by staying along the inside of the channel). Then use a template bit on the router to trim the extra wood off after the piece is removed.