You can query the max texture size yourself if you want to check:
https://www.khronos.org/registry/OpenGL-Refpages/gl4/html/glGet.xhtml
eg
GLint mxSize;
glGetIntegerv(GL_MAX_TEXTURE_SIZE, &mxSize);
Current OpenGL specification indicates this must be at least 1024, but older versions will specify a different size. For example, a 2.1 compatibility context specifies this must be at least 64 (yeesh).
If you have even a halfway decent GPU, you should be able to load large textures.
My NVidia 980M, for example, gives 16384.