Yes, a (decent quality) blade grinder can do an acceptable job at a fine grind.
Blade grinders don't do well at coarse grinds: if you try you generally get a very uneven grind. But for find grind, you run it longer and generally get a sufficiently even grind. You don't have the same degree of control over the grind as with a burr grinder, however. You have to experiment with how long to run your grinder for a given quantity of beans. You also have to be careful not to run it too long and overheat the beans.
I like to drip coffee and use a blade grinder because it was cheap and I don't mind if the taste is somewhat more bitter than it would be with a coarser grind. I use about an ounce of beans and grind it for 12-15 seconds.