fWell here are some potential problems for on-line shopping that I've noticed:
Transportation heavily depends on courier and mail services which could lead to unexpected problems and sometimes experimentation may be necessary in order to find the best way to have components shipped. One time I ordered a power supply and some components from a web-store. It turned out that they didn't have some of the miscellaneous stuff I ordered, so we agreed that the main part of the order be shipped via one of the leading courier agencies and have the rest sent by regular mail once they get the items. I of course paid for express shipping and 3 days later the packet was at my local airport. It took shipping company 3 weeks for the packet to travel from the airport to my address. First there were customs problems because nobody knew under which tariff category ordered items belonged, after that I got sent customs processing certificate for female underwear instead of electronic components so I had to complain to the shipping company and it took them 5 days to dig up my own customs certificate and after that some items were wrongly processed and so on and so on and so on. In the end, I got the regular mail back-order before the expressly shipped main order! Fortunately, I wasn't in a hurry, but imagine you have a project with a deadline and what ws supposed to take 4 days takes 22 and after that you haven't even begun to do any work!
Next problem can be shipping costs. For example Digikey charges $120 shipping to my country while I can get other stores to ship for $20. Of course, for large projects, this isn't a problem.
Next problem could be returns policy. Some stores won't pay for return shipping and sometimes shipping can be as expensive as ordered articles. Plus, there's the time wasted which needs to be accounted for as well. Of course, there could be problems with customs too.
Next problem could be details. There are lots of little things which can become a big problem and which sometimes can't be detected in advance from datasheets or information available on the website. Of course, this can be solved by sending few e-mails, but sometimes people make assumptions. I heard of a guy who one time ordered a large number of potentiometers. There are washers and nuts available as accessories for those potentiometers. In my country, potentiometers made by that manufacturer always come with a washer and a nut, but in the datasheet they are listed as optional accessories. Ones which he got from the Internet didn't have any nuts and washers, so he couldn't mount them and had to pause the project for some time until he managed to obtain the washers and nuts. The problem was that he assumed that he'll get the optional nuts and washers. Similar problem can occur if you’re looking for specific revision of a certain IC or something similar.
On the other hand there are problems with buying components personally too. Will the merchant have enough time to dedicate to you as a customer? Employees can be overworked and tired and could be misinformed and so on and so on. On the other hand, would you be able to make a right decision quickly enough? If you're traveling to another country, you're likely going to have a set of objectives which you need to accomplish and are likely to be under pressure to get everything done in the limited time period which you're spending in that country. If everything goes according to plan, you might as well have stayed home and made order over the Internet, but if something comes up, will you be able to manage the problem? AngryEE's list is a great example of that.
Next, you speak of China as if it's San Marino. Are you sure that companies you need to visit are in the area you'll be visiting? If you're going to visit several cities, time pressure problems may turn out to be even worse than expected.
I know that my answer isn't too helpful, but I least I managed to provide some food for thought.