Yes. But hard aspects are traditionally considered with mathematical points like midpoints in charts to produce strong, irresistible, palpable energy and may even drive events. With the soft and/or minor aspects like your semi-sextile, it’s more likely to be an unconscious feeling, something you sense and is unlikely to be expressed externally.

Personally, I like using the Sun/Moon midpoints when looking at relationships. Years ago I read (sorry I don’t have any good book recommendations), the Sun/Moon described as the point where ego = emotions, producing absolute contentment. By sign and house, it reveals where a person is likely to feel most happy. So when triggered by synatry, progressions or transits it can produce a euphoric feeling or events particularly when coupled with transits. To me, midpoint analysis, gives the final touches to understanding a relationship, but they do not trump planet/angle aspects or house overlays.

In synastry, I think the Sun/Moon person feels the energy more than the planet or angle person. When it goes both ways it can feel magical to both people. So Sun/Moon = Venus: the expression of love by the Venus person might make the Sun/Moon person feel deeply loved and happy.

My romantic interest and I have:

He: Natal Sun/Moon midpoint at 24 Leo
Me: Natal Sun/Moon midpoint at 24 Libra
Us: Composite Sun/Moon midpoint at 24 Virgo

Last week when Transit Jupiter Retrograded at 24 Sag, (soft aspects to Natals) we both felt a deep inner awareness of “how much I need you”. I am as yet to see how the hard aspect might externally manifest over the next 4 weeks when Transit Jupiter is 24-23 degree square our Composite Sun/Moon.

There’s also a lot of past posts on this topic you could do a site search.

I consider them when looking at transits. 

There are a couple of books on them that I know of / have read.  

Midpoints: Unleashing the Power of the Planets Midpoints: Identify & Integrate Midpoints Into Horoscope Synthesis

Good luck!

I mainly consider conjunctions and oppositions to midpoints as significant, sometimes squares too but as secondary.

I also find that looking at someone's mid-point chart gives you a good idea of their dominant sign energy influences. Someone who has a lot of watery midpoints may be more watery/emotional than they seem just based on the natal. My midpoints are overwhelmingly watery, over 50% in water and the rest divided almost equally in the other elements. Explains a lot considering I lack water in my natal chart. I feel a lot but can't express it. 

Calliope said
 

If someone Sun/ Moon Midpoints is 24 degrees Virgo and I have 24 degrees Venus Leo, does this mean my Venus aspects their Midpoint? Did I get this right or wrong?

  

This is a more complicated technical question but I'd say you got this "wrong." It's not having a planet at 24 degrees of any sign. The most important contacts for a midpoint are "hard" aspects: conjunction (0 degrees apart), square (90 degrees), opposition (180 degrees). If you had Venus at 24 Virgo, 24 Sagittarius, 24 Pisces, or 24 Gemini, that would be a significant aspect.

I'd even put the semisquare (half of a square, or 45 degrees) and sesquiquadrate (135 degrees, or "a square and a half") down as reasonably potent "hard" aspects. A bit more math required, but for a midpoint at 24 Virgo, you're looking at 9 Leo, 9 Taurus, 9 Aquarius, 9 Scorpio.

What you have here is a "semi-sextile," or half of a sextile. 30 degrees apart. That is an aspect but, at least in my view, it's less important as a "hard" aspect involving a key midpoint than the ones I mentioned above.

Some midpoints are very important. Sun/Moon, Venus/Mars, etc. There's a site out there where you can calculate all your midpoints and get a list running through the whole zodiac. Then you can see if any of your planets, or those of people close to you, or the transiting planets in the sky right now, are making important aspects to any of your midpoints. It's fun to check it out.

Is there any significance to two people having their sun moon midpoints conjunct?