No, the size of the barrel has no effect. The only thing- the drum/bucket/barrel, etc. can not have any leaks. The top and all fittings, etc. must be absolutely air tight, otherwise it will affect the cyclonic separation and a lot more dust will make it through to the shopvac filter.
FYI, if you are able to connect it as a push-though where the mini is downstream from the shopvac (not usually possible with most shop vacs), you can just attach a plastic lawn& leaf trash bag to the bottom to collect the dust and chips, since the cyclone is under positive pressure.
How would this be accomplished, blower side?