I may be wrong - and I'll stand corrected if I am - but my experience of this type of situation invariably results in the cancellation of your IFR clearance (in the US at least). Therefore, you are no longer flying in accordance with IFR and must remain in visual conditions.
That makes sense when you consider that on request of a "visual" you [the pilot] are declaring that you can commence an approach in visual conditions and have your landing runway in sight at all times during that manoeuvre. Furthermore, you may now be off any published instrument routing for the approach (you may be on a left base) and probably won't be given vectors unless there are traffic considerations. But beware of fog or other obscurations that may make visual approaches difficult or impossible in the latter stages!
So, if my memory serves me right (not always) your IFR gets cancelled at the commencement of a visual approach.
One other situation that I have experienced is being offered a visual whilst at some distance from the airport. On acceptance you are given radar vectors to some point where you can state "field in sight" and continue from there.
These are just situations from my personal experience and I don't doubt that different countries have different ideas on this.
Thanks
df1