This is so hard to figure out ...yes there is a file size reduction in MB due to compression when uploading to a picasaweb album (for G+ users) for no G+ users there are options that allow uploading preserving original quality in the picasa 3 application 

But if your prints from a print provider are a horrible quality, this is usually down to the pixel size of the image, rule of thumb is 300 pixel per inch example this image   https://lh6.googleusercontent.com/-8QV-6lxqaiQ/TS8jPxDz2_I/AAAAAAAAlP8/Z-WY-sorYI4/s0/IMG_5481.JPG is 1600 pixels on the long side (and about 100kb) but should print just fine as a 6x4 ..if I printed a larger photo then yes quality of print would be reduced