No. 300 DPI printing is not the same as 300 DPI on screen, because one dot on screen can be multiple colors (depending on the color depth, typically 16,777,216 can be expected), while one dot on paper is, well, either black or white. So for the same DPI, screen outperforms paper. 250 DPI on screen will definitely beat 300 DPI on paper.
After a quick search, I see you can get a 1200 dpi black and white laser printer for less than $100. Colour printers can overlay colours or pre mix the ink.