>>Would that make a difference in the end result of the image quality or in the budget?<<
No and Yes.
No difference in image quality, but a big difference in cost.
If the print job uses a spot colour such as a PMS, then that specific colour ink will be used in the press. Plus the black, so two plates and two runs through the press, with one washdown between. If you use the CMYK equivalent of that spot colour, all four process colour inks will be required. Four plates, four runs, so more expensive.
How will you be sending the file to the printer? As a native AI file? or as a PDF? If the printer hasn't told you what is preferred, ring them and ask.
If sending as a native AI file, it is usually a good idea to make a copy of the file and convert the text to outlines. Then the text becomes a graphic, so there is no need to also supply the printer with the font.
But again, check with the printer.
If he requests a PDF, make sure you get the preferred job options settings for Distiller from him. This can be critical.
If you need to know more, post back.