No, one would normally capitalise the V in these circumstances. However, it is possible that the sentence
"e e cummings was a poet who never used capital letters."
is grammatically correct, as he was known to spell his name in precisely this fashion. Wikipedia notes that modern scholars tend to spell his name in the normal way, and that there appears to have been some scholarly dispute over the form that the Cummings himself preferred.
In a similar vein, one might look at recent Apple product naming conventions to see another possible example, such as
"iTunes is a music management application that copies music onto iPads and iPhones."
Having quickly scanned the Apple web pages they seem to be very careful about not using an "iWord" at the start of a sentence, possibly to avoid annoying grammar pedants. Personally I regard this as an objectionable neologism and usually refer to their devices in written communication as "the Ipad" etc., but if you're prepared to accept Apple's wanton tinkering with the rules of grammar, it would certainly be more odd and wrong to start a sentence with "ITunes is ...."
A further example from the world of computing would be Hungarian Notation, which uses a lower case prefix to indicate the type of a variable in languages with strong typing, such as C. So the age of a person would be stored in an unsigned long integer, and referred to as "ulAge". Capitalising the first letter of this variable would be actively confusing, since C is case sensitive, and "ulAge" and "UlAge" are not interchangeable. This then gives the following possible sentence.
"ulAge contains the user's age in years."
I would suggest that having a capital letter at the beginning of a sentence is a sufficiently hard and fast rule of grammar that you, like Apple, should seek to avoid any unusual situations in which it might be broken.