Can the Ego 21" self propelled mower cut 1/2 acre on a single charge?

With the 7.5 battery it is possible to get 1/2 acre lot done.  If not you can certainly use the battery from your blower.  It will depend on the thickness, length, and moisture level of the lawn.
My lot is about 1/2 acre (but then there is house and other non grass areas) and I have mowed the entire yard on a single charge.
All Ego batteries work in all Ego tools.  If you have a 2.5 for your blower you will probably get 10-15 minutes of mowing from it.

It really depends upon the thickness/height of the grass, but if it's really 1/2 acre of all grass, I predict you'll need to charge your battery once halfway through unless you mow frequently enough so that you are only chopping an inch off the top.

I live in Florida and only mow once a week, so with the summer rains/sun, I'm chopping several inches of grass every time I go out. My experience (with a 1 year old battery, and high lift blade, with relatively thick grass) is around 1/5 acre per battery charge, or 8,500 sq feet. That's 66′ long by 130′ wide, (8,500 sq ft, or just under 1/5 – 0.195 acres ).

The best I've ever gotten is around 1/3rd of an acre on a single charge (light grass in the winter). 
You may get better performance without a high lift blade, especially if your grass isn't very thick and is bone dry.

FYI - I get 7-10 minutes of run time from a 2.5 AH battery in my mower, with relatively thick grass and the high-lift blade.
(I just bought a second 7.5 AH battery so that I can mow larger sections of my lawn in a single session.)

SummetJ’s experience is close to what I’ve experienced - BUT, I’ve only used the HL blade the last time to cut .22 acres. Also live in S. Florida where it’s been raining a lot. YMMV