No. And even if you did know, it doesn't necessarily give you much indication of the cost - there could be other special engineering difficulties in connecting you.
The fact that you're only getting 15Mbps on FTTC suggests that the cable path between you and your cabinet is much longer than you think it is (probably over 2km), unless there is a gross fault somewhere. Compare with what the BT wholesale broadband checker says.
However, your FTTPoD desktop quote is relatively low, which is good news. Of course it's possible that it's in error, or that OpenReach have been tuning the process to give more accurate initial quotes.
If as you say you are "desperate" to improve your speeds, and assuming you would be happy to pay a final price of £4K-£6K+VAT, then you'll have to gamble the £250+VAT to find out. The gamble is partly that the price ends up being higher than you're willing to pay, and partly that native FTTP turns up in your area in a year or two anyway.
If i pay for the real quote does that tie me into any firm commitments for the order and can you cancel if its too expensive?
Upon paying the £250+VAT you are technically placing an order, but you are not committed. Once you receive the confirmed quote you have 30 days to make up your mind. If you do not proceed then the order automatically cancels, but you lose your £250+VAT.
Also do you have to pay the full quote amount up front before the work starts?
Yes, minus any voucher support you're eligible for (which will be collected on your behalf by the provider once installation is complete). Also, the £250+VAT you've paid will already have been deducted from the quote.
If you are eligible for a voucher, do apply for it at the same time as you place your initial survey order. This uses the time effectively while you're waiting for the survey to take place.