No you dont. The Holts TyreWeld, apparently identifies that it can be washed out of the tyre very easily by many nationally recognised tyre companies. Apparently it causes no harm to the tyre, and the likes of repairable punctures, can still be resolved and driven upon.
Some people have said that using it for a long period of time (or leaving it in the tyre for a long period of time) it apparently eats away at the rubber. There is no definite proof that it does, so you will read some horror stories on it, but take them all with a pinch of salt. I suspect only if people use cheap and nasty tyres in the first place will these products cause problems.
The National Tyres Distribution Assosciation support the product, and most suppliers will indicate on the listing of the product it can be washed out (from what I remember it says it on the tin