In my opinion those accelerators are not effective. They basically broadcast your transaction to more miners... but transaction broadcast is not a problem after 6 hours of broadcasting.
it depends on the "accelerator" that is being used. majority of them are scams, specially those that ask for money. they don't even re-broadcast your transaction. they are either getting views for their site or ripping people off (taking money).
there are some cases that the miner has put up that option and for free like ViaBtc and Bitmain where the offer is real but with limited number of txs accepted. they do put it in their custom queue and mine the transaction.