I haven't use Velcro in that manner to hold a screen but have used a lot of self stick Velcro. I think a complete strip around the screen would be very hard to get up without wrinkles. To do it you would be doing a lot of sticking and un-sticking of the strip. Most of this Velcro really sticks together and when pulling it on and off you will lift the glue from the wall I think. Or pull the paint. You will also have a raw edge of screen material at the edge and I'm not sure how that will look.
A friend of mine used double sided tape on a similar idea and got lots of waves. He later went to a contact cement had the screen very flat and 6 months later lots of waves. His experience is what prompted me to build the tension screen I have linked below in my signature below.
But if you want to know if it will hold it up the answer is yes.
I also don't like the black boarder look and made a framed screen that floats off the wall. I personal think the look is good and will blend with the room if the screen color goes with the wall color.
In my ideal world I would go totally stealth and using one of the DIY paints in the DIY forum and paint out the entire wall with a more screen friendly paint than white and use the wall as a accent wall. But I like stealth others like the wow factor of seeing the big framed screen when not in use.