Not particularly. Charles X was also something of an isolationist; the conquest of Algeria took place against the July Revolution you must remember, and was purely a political move by Charles X and his royalist supporters to try and bolster their position. Now, his elder brother, Louis XVIII, was of course an entirely different man, who ordered the Hundred Thousand Sons of Saint Louis partially to put down the threat of dreaded liberalism (the horror!) spreading from Spain, and partially to put Ferdinand VII in his pocket. Notably however, the expedition was headed up by the duc d'Angoulême. Now, while Louis Antoine was certainly more militant than the rest of his family - he, unlike most of the rest, actually fought in the Napoleonic Wars - even he wouldn't likely turn against the Prussians, who are, remember, a crowning power in the Quintuple Alliance. Beyond that though, it's very unlikely Thiers would ever become a minister under the Bourbons.
Basically you're going to need something like the June Rebellion to be successful, and that is going to be a very far bridge to cross.