Hi Elaine and welcome to the forum,
Yes, nature of the business to see most drop-shippers for the majority of virtually anything coming from China these days.
I think you will find it's a mixed bag, if you are upfront as to your products location (as you are required to be when using eBay to list for example) then that eliminates any major drama because people who do have an issue, whatever it may be, will simply pass you by as supply option.
I don't think there is any real stigma attached to buying from China anymore, at least not from the majority of customers. The main concern most will be looking at is shipping times and this is where most of the problems can be with using a Chinese supplier.
So if you do use China as a supply resource, then ensure you use a supplier with the quickest possible shipping times to mitigate that becoming a problem with customers. Outside of that concern, you would really just be joining the cue of 99% of other Drop-Shippers using China as their supply resource :)
Having said that, yes, you do still need to be careful quality wise. The thing about China is that you can get anything made for pretty much any amount you want to pay. So that ends up creating a supply chain with varied quality. So cheap in China can quite often mean cheap, as in quality as well. Now it really depends on the customer market you are targeting.
If it's the low-end bargain hunters, then cheap quality is something people will usually accept so long as the price matches. If you are targeting a middle to higher end customer market, then I would be suggesting buying a few samples for yourself to test out before launching into a full-on sales blitz of any kind.
Remember, what it comes to Drop-Shipping, it's your reputation as a supplier that you need to protect if you want to be in this game long term. So always have that front of mind when considering dealing with suppliers. It's just a harsh fact of this business model, but many, if not most, suppliers will simply not treat you the same as they would if you were a Wholesale customer
So my advice, look for a supplier that will give you the exact same level of service as you would expect as a Wholesale customer. If you can't get that. then it's your own trading reputation you are putting at a higher risk than you probably should!