Burning tokens doesn't guarantee the value to go up, that's for sure, supply can be of one token but if it has no real value I don't see its valuation can go up (like the Aurora token, it's worth nothing despite the supply)
Of course not, especially now that the ICO market is in bad condition and prices dont go up once tokens are on exchange but its still the better option for what to do with unsold tokens.
I consider the burning of tokens to be a good solution, which can positively affect the result of the value of coins. However, the fashion team send these tokens also to the reserve.