I ran my veritas (88dB/W/M) minimum 4ohms for a while with just the 3805, and then with a 200WPC amp and a 300WPC amp; and did some comparisons including taking current and voltage measurements. Then I did the same with my 4308 and then with my current AV7005. I can tell you I feel my speakers sound better/louder/quieter with the amps but I won't because I know I am not sure about that but I am sure I will fail any sort of blind tests let alone double blind tests.
If you want to feel good about having an amp, more headroom, and/or have a larger room (>2500 cu.ft.) go get an amp and don't look back. Or if you have a smaller room and believe in science and engineering, then be happy with the 3805. No the Studio 40's are not difficult to drive, Paradigm tech support will tell you that, and they cannot play loud anyway. So if you give it 200 to 300W it may sound better depending on the types of music you play and even then it will only be for some peak durations. The fact is, they are rated for only 140W maximum input power, not continuous. Their estimated in room sensitivity is 92 dB 8 ohm compatible whatever Paradigm intended that to mean

, presumably per watt per meter so again, relatively speaking they are not hard to drive at all but they are not dsigned/built to play loud given that they are small and cannot handle much power anyway.
Studio 40 - Welcome to the New Official Paradigm® Website.
Bottom line, is, no it won't sound noticeably better in a blind listening session with and without an external amp but more power never hurts. If you want to have more noticeably SQ improvement, trade up to the Studio 60 V5. I can assure you that the 3805+Studio 60 V5 will sound much better than a 300WPC amp+Studio 40 V3, no doubt in my mind about that at all. Electronics are relatively cheap so people are tempted to take the short cut, get a powerful amp and convince themselves their speakers now sound good, when in fact they should bite the bullet and upgrade their speakers if they are serious about better sound quality.