Most typically remove the file shortly after the conversion process completes, while some will state exactly how long it'll be accessible; however, there are always exceptions to ever rule and site. So if it's very sensitive to you then be careful or obtain a jpg to pdf converter and convert offline.
Some sites also do this. I have a file conversion script I use with Adobe Photoshop, it handles quite a few of the above. I can import one of the images into my PS file, run the script, export PS to PDF and then open it in Adobe Dreamweaver. Here's an example; if my image is 640px x 960px, I run the script, and it will give me a file like this; Now I save to PS and open that in Dreamweaver, this is what I get; That was fast, as simple and as much as I'd like to, I'd like to go one more step and use some above scripts with a different website. So I created the scripts and included them and have a copy of this in my scripts folder with the links. I'm sure there'll be more examples in the future so be sure to check back for them! I.