Question regarding smart objects (resizing to big or small) and will it lose quality when printing?

It's not possible to resize a pixel image without losing quality. Some algorithms may produce better results than others in some cases; others in other cases. But there will always be some quality loss. You either throw out pixels, or invent new ones. No software can change that basic fact, not On1 and not Topaz.

The point of smart objects isn't that there's no quality loss. This is often misunderstood. The point is that you don't get cumulative degradation with repeated transforms. You only get the quality loss once, when rasterizing the smart object. Which you have to do sooner or later.

A smart object has a copy of the original full-size file embedded at all times, so that all transforms refer to that full size copy. You start fresh every time, instead of having to build on previous transforms.

Until you rasterize. Then you get the normal quality loss that comes with resizing and resampling.

Vector files can be infinitely resized, because they're made from mathematical formulae, not a grid of discrete pixels. But then you need to go to Illustrator.

Oh, BTW, 12 x 15 inches at 300 ppi is 3600 x 4500 pixels. A web image is typically 1000 - 1200 pixels on the long side. This massive upsampling isn't going to work. You'll get an image, but I can guarantee you it won't look good. I think you need to find another way to do this. Get high resolution images from somewhere else. Web images normally aren't usable for this.

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The main reason I ask is because, there are a few programs like On1 and topaz that will resize an image without losing quality. 

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Funny. 

Those applications may provide better results when upsampling images (in many cases at least) but to do that they have to create pixels and the image is still changed, even if you think it is qualitatively unchanged. 

Downsampling is generally less of a problem (and one can add a little sharpening afterwards as a Smart Filter if necessary), upsampling is an issue. 

What effective resolution do you need anyway? 

So when I drag and drop that image (300 ppi) to my document and convert it to a smart object

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Why don’t you drop it as a Smart Object right away? 

What is »my document« exactly?