The short answer is yes, you can make points smaller than 1.0. There could be a few different things going on:
(1) Are you in map view or layout view? The map data view may be scaling your points so that they appear the same size as you zoom in.
(2) It is very difficult to eyeball the difference between 1.0 and 0.5, for example. On my screen they look the same (both just tiny dots).
(3) Finally, although you may want to display more points, it is worth considering if you should generalize a copy of your data for display. A size of 1.0 points (the measurement, not a point feature) is equivalent to 0.014" (0.03556 cm), also known as 'very small'. I have displayed points down to 0.4 as a test, but would not put this on a map. As a side note, below 0.4 the point disappeared, so maybe ArcMap has a minimum size to display.
You may find these links useful:
Fonts in ArcGIS
Understanding Font Size