The Thiers Issard paste is a mix of aluminium oxide and diamond particles in a wax binder, said to be the equivalent of using a 10,000 grit stone. It should be fine for touch-ups, and much prolong the amount of time between honing sessions on a stone, but won't replace a stone of course: over time the "give" or slackness in a strop or paddle will round the bevels on the razors edge, and they will need to be re-set. Over-use of the paste will hasten this rounding. Hanging strops, because there is more slack, will cause rounding of the bevel quicker than paddles: it is of little consequence when no paste is used as there is very little abrasive effect from just plain leather, but becomes a factor when an abrasive compound is used.
In itself, a little rounding doesn't hurt - in some cases it might even be seen as a good thing - when stropping wedges, for instance. Even an unpasted cotton hanging strop will round an edge in time, much quicker than a plain leather strop will. To decrease the rounding effect for ordinary razors a stiff paddle should be used - unless you like honing on stones pretty often, of course.
What micron size are the diamond particles in TI paste? The micron/grit tables are often conflicting. Depending on which table you look at, a 10,000 grit stone has an equivent micron size of 1.4, but some sites say less than 1.0 micron (which I find hard to believe as the Shapton glass stone rated at 12,000 grit has a micron size of 0.92 printed on the bottom). Chrome oxide should, theoretically, give a much smoother edge - being rated at around 0.5 microns an equivalent stone would be something like a 30,000 grit Shapton. Aluminium oxide (type A, presumably) comes in a whole variety of micron sizes, but for the TI paste to perform at somewhere near the level of CrOx, I would expect it to be around 0.5 - 0.25 microns in order to smooth the edge left by the diamond particles.
Regards,
Neil