I am making an image to be printed on a 3x4 foot poster.
I am worried that the image will be pixelated after being printed. Should I use svg to make this poster? Is this even a valid concern?
You want your image to have the correct source resolution for the print. If your print resolution is going to be 300 dpi (dots per inch), then for a 36×44 inch poster, you need a 10800×14400 pixel source document.
I wouldn't print a document with a resolution of less than 300 dpi. So, unless your source image has 10800 by 14400 pixels, then you will see pixels in the output, because you have to upscale it.
It depends on your source though: So, let's say you have a photo from a digital camera that is 1080 by 1440 pixels, then you have to upscale it by a factor of 10 to even get to the print resolution. Most upscaling algorithms will try to "blur" the image a bit*, so you don't get pixels, but rather a smooth transition. This however will make your result look a bit unsharp.
If your source is just text or graphics created in your graphics program directly (e.g. Photoshop), then you don't need to upscale anything and can work with the huge resolution right away.
Also note that the size of such an image is huge (raw 445 MB as you can see in the screenshot), and not all computers will easily handle such a high resolution.
* Actually, they will interpolate pixels, not blur it. See here: Image Scaling.
SVG graphics on the other hand are vector graphics. You can upscale vector graphics as much as you want, and it won't be pixelated when printed, simply because there are no pixels involved.
However, your source has to be a vector graphic too. You can't turn a photo into a vector graphic — simple graphics like logos and text however work fine, but you need to have them as a vector source already. Many companies or designers will provide sources as SVG or EPS files, which are vector-based.
And, as I mentioned before: Text and graphics created in Photoshop or similar programs are handled as vectors internally. Before you finally render your image, you can always change the dimensions of lines, squares, fonts, etc. (unless you specifically choose to "raster" them, which means turning the vectors into pixels).