Ideally, yes. But it often depended on where the shipments came from. For example, in coffee from Brazil, the 1800 measure used (according to the trade discussion of the US Consul in 1880) was the arroba, which was about 14.7kg (Portuguese standard) and not changed until 1874 when a bag was redefined from 5 arrobas down to 60kg. However, this was not a universal measure. The arroba in Spain and former Spanish colonies was also different in weight by a good amount, being less than 12kg, and they all varied a bit from one another too. This problem of variable weights and measures was one of the economically minded reasons that the SI units eventually came into use, and why most governments tackled the issue actively for their own preferred measures (as well as other standardizations, such as time) in the mid and late 19th century. But for the era you're looking at, it had not shaken out in a way that those not directly involved in the trade could easily evaluate.

There are some standards: British and US import/export records for sugar (and sometimes for coffee) refer to hundredweights (cwt., which at that time was commonly 100 pounds in the US but often 112 in Britain--only resolved by Act in 1824 yet still creating enough confusion that the word "cental" had to come into use for the US cwt) and also to hogsheads/puncheons as well as casks (volume measurements more than weight, though sometimes you'll see various average weights ascribed to them). These were a little more standard but still unreliable, especially when not used for vintage or molasses. I do not really see "bag" used for sugar, though.

I just asked one of my colleagues (the Britishist, sorry), and he suggested looking at excise duty if you know it, to determine just how much of something there really was because they tended to use weight. But of course that requires that we trust the collector and his instruments too, and that we pick a time and place where duties were actually in effect. Those rates are available for England for 1824, but I haven't had any luck (at least not online) for the US because it was a bit uneven. Charles Griffin way back in 1897 wrote an essay on the taxation of sugar that may get at some of these problems, but it may also provide a few helpful answers on sugar trafficking. (Hopefully it's not behind the JSTOR paywall section, but if it is, you may find it via Google Books under the journal title, or I can arrange to obtain it on your behalf.)

All of this is ultimately to say "it depends," though we can probably get within certain margins of error and tackle the quandary with a little sleuthing. Do you have examples of origins and destinations with quantities you need, or document images? I've got some connections to people who work on 19th-century weights and measures (I mostly work on units of distance, time, and energy) so I can ask around. Of course, other flairs who work in the history of science and technology may know more than I do on this point.

[edit: Tried to clean up my grammar there, sorry.]