^no.
assume starting price of £100.
Add 17.5% = £117.50
Then, if you try to subtract 17.5% from the £117.50, by multiplying by 0.825, you get an answer of £96 or so, not the £100 as it should be.
To get back to the £100, you have to multiply by 0.851 or something (i.e. removing 14.9%).
Try it.
As I said, though, I'm not sure the way the government does it- but the maths suggests they should do it my way, although they might not.
EDIT: basically, the easiest way to look at it is, 17.5% of £100 (original pre-VAT price) does not equal 17.5% of £117.50 (Post-VAT price).