Would have to do the math to be sure, but doing some quick simulations in my mind - I believe you're correct, modulo the impact of the orientation of that force changing (Earth goes around the Sun). Let me illustrate with a diagram:
PROGRADE
(raise apo)
|
+--------------+--------------+
| |
| -> --->--- -> |
+- -> -/ \- -> -+
-> / \ ->
/ -> / /II\ \ | -+
+----+ -> | |IIII| | | +- IN SHADOW
| \ -> \ \II/ / | -+
| -> \ / ->
| +- -> -\ /- -> -+
| | -> --- |
RADIAL | |
IN +--------------+--------------+
(also raise apo) |
((I think...)) RETROGRADE
(lower peri)
This shows a body in orbit (the empty sphere) around the body (the filled sphere). The orbit goes clockwise, sun radiation comes from the left, arrows illustrate the acceleration it creates on the body. Simulating it in my head, I believe such setup would lead to the orbit getting elliptical, with the apogee getting larger and the perigee getting smaller, all the way until either the perigee hits the atmosphere or the body reaches escape velocity (thanks to small, but unbalanced contribution labeled RADIAL IN).
I'm not sure how long such a process would take for a satellite not designed to exploit solar radiation for propulsion, nor whether it wouldn't be dwarfed by other orbit-disturbing influences such as the Moon and other planets.
Also: aerobraking a highly elliptical orbit isn't going to leave you much of a satellite to find.
(Note: I studied orbital mechanics in university on Kerbin, under Jebediah Kerman, so I might be wrong here.)