A much-quoted guideline is that, if you can get good reception of Channel 5 (and, of course, the postcode checker says that you're in a Freeview area), then you should be able to get Freeview.
However, when I bought my Freeview box a few years ago, the postcode checker said I was outside the reception area and I could hardly get any sort of reception of Channel 5. Despite this, the Freview box worked perfectly.
The vast majority of people, with external aerials, find that they don't need to upgrade. Just ask yourself how often you see an aerial fitter, up a ladder, installing a new aerial. If most people needed to upgrade, you'd see aerial fitters on every street but I haven't seen one at work for ages.
As Pea Pod indicates, you won't know until you try.
Chris