If they could manage it, and quite frequently. I'm going to talk about Laon because it's the example I know the best.
Laon was an important intellectual center in France from the Carolingian period, and it became particularly important in the late eleventh century when Anselm of Laon took charge of the school there. Anselm is credited with the creation of the Glossa ordinaria, the gloss or explanation of the Bible which was the primary text for the introduction to biblical study for four hundred years. He was even one of the first teachers of the brilliant, controversial Peter Abelard, who not only was the first great vocal advocate for the use of Aristotelian logic, but seems to have also inaugurated the long-standing tradition of undergraduates thinking their professor is an idiot. In this period, the city of Laon began to have some severe disagreements with its bishops, who were the lay and spiritual rulers of the city. This came to a head in 1112 when the townspeople, taking advantage of Bishop Waldric's temporary absence, sought and received a communal charter from the king of France. When Waldric returned, he attempted to suppress the charter (also seeking the king's help) and for his troubles he was murdered in the Laon cathedral at Easter.
Walderic's successor, Barthélemy de Jur (sometimes erroneously called 'de Vir'), perhaps mindful of Walderic's fate, gave the commune his tacit support. Peace and political stability at home also meant that Barthélemy could spend his time checking the behavior of the northern French castellians, who were represented some of the worst examples of medieval feudal privilege and violent excess. Barthélemy spent a great deal of his time encouraging the foundation of monasteries in his domains, which in turn provided the lords with a way to show their piety as well as strong, stable economic centers in the region.
However, after some 40 years as bishop, Barthélemy was forced to resign and retire to the Cistercian monastery of Foigny in 1151, which he had helped found. His successor, Gautier de Mortagne (r.1151-1174), quickly set about to undermine the commune. Indeed, he even brought suit against Barthélemy the monk, claiming he had given away more of the episcopal patrimony than he ought. From this point on, the bishops of Laon either were coolly neutral towards the commune or actively opposed it. Both sides often turned to the king, who had, after all, granted the charter, for help, and the king gave it to each side as was politically expedient.
The area around Laon was relatively peaceful from the late twelfth century until King Philip le Bel began a series of wars in Flanders in the fourteenth century. The economy, thanks in part to Barthélemy's monasteries, was doing very well, and the lords had the Crusades to keep them occupied. However, the commune of Laon still faced threats not only from the bishop, but also the local nobility. These lords did not directly threaten the integrity of the commune (usually), but instead undermined its authority by simply refusing to cooperate. One of the lords of Coucy, Enguerrand IV (d. 1310), was particularly vicious, to the point at which he was once imprisoned by Louis IX and, in an act that set legal precedent, denied trial by combat.
Similarly the cathedral chapter, the members of the cathedral clergy who were not the bishop, constituted another political force which sometimes allied with the commune and sometimes opposed it. This trend intensified as the canons of the cathedral, who had previously been the teachers at the cathedral school, were slowly replaced by political careerists. We can see this latter from the second decade of the thirteenth century, and the school at Laon finally falls apart in 1229 with the death of its last great exegete. By the late thirteenth century, holding the position of canon in Laon is a very important step on the career ladder, and several popes of this time held such a position before their election. Which side the canons were on were on depended on their relationship with the bishop. For example, when they were in conflict with Bishop Anselm in the 1230s, the canons appealed to both the king and the local commune for support.
This unsteady political balancing act between various forces lasted into the fourteenth century. By this time, the kings of France had consolidated their rule and even subjugated the papacy. Finally, in 1331, the commune of Laon was dissolved by royal decree with scarcely a whimper.
So, to sum up: locations granted royal charters of self-governance could indeed be completely free of outside interference. This was a right which they had to actively protect, and sometimes they were unsuccessful. The relative autonomy of any such city varied greatly with the passage of time, and holding the right did not guarantee that it would continue to be held.
Some sources; most are, unavoidably, in French:
Martinet, Suzanne. “Un évêque bâtisseur: Gautier de Mortagne.” In Mémoires de la Fédération des Sociétés d’Histoire et d’Archéologie de l’Aisne, 81–92. 8. Laon: Fédération des Sociétés d’Histoire et d’Archéologie de l’Aisne, 1962.
———. Montloon: reflet fidèle de la montagne et des environs de Laon de 1100 à 1300. Laon: Éditions de l’Impr. du courrier de l’Aisne, 1972.
Flint, Valerie I. J. “The ‘School of Laon’. A Reconsideration.” Recherches de Théologie Ancienne et Médiévale 43 (1976): 89–110.
Picó, Fernando. “Changements dans la composition du chapitre cathédrale de Laon (1155-1318).” Revue d’histoire ecclésiastique 71, no. 1–2 (1976): 78–91.
———. “Membership in the cathedral chapter of Laon, 1217-1238.” Catholic Historical Review 61, no. 1 (1975): 1–30.
Foviaux, Jacques. “Les sermons donnés à Laon, en 1242, par le Chanoine Jacques de Troyes, futur Urbain IV.” Recherches augustiniennes: Supplément à la Revue des Etudes Augustiniennes 20 (1985): 203–56.
Bur, Michel. Histoire de Laon et du Laonnois. Pays et villes de France. Toulouse: Privat, 1987.
Saint-Denis, Alain. Apogée d’une cité : Laon et le Laonnois aux XIIe et XIIIe s. Historie et archéologie médiévale. Nancy: Pr. Univers., 1994.
Doyen, Bénédicte. “Le rôle des monastères dans la mise en valeur des terroirs de Thiérache : l’exemple de l’abbaye cistercienne de Foigny (XIIe-XVIe siècles).” Mélanges de sciences religieuses 60, no. 3 (2000): 45–62.
Tétart, Jean-Louis. “Barthélemy, évêque de Laon, moine cistercien de Foigny.” In Mémoires de la Fédération des Sociétés d’Histoire et d’Archéologie de l’Aisne, 7–20. 46. Laon: Fédération des Sociétés d’Histoire et d’Archéologie de l’Aisne, 2001.
Falkenstein, Ludwig. “Die frühen Urkunden der Bischöfe von Laon: Anmerkungen zu ihrer Edition.” Revue Mabillon: Revue internationale d’histoire et de littérature religieuses 15 (2004): 217–22. doi:10.1484/J.RM.2.303557.
Brunel, Ghislain. “Les hommes de corps du chapitre cathédral de Laon (1200-1460): continuité et crises de la servitude dans une seigneurie ecclésiastique.” In Forms of Servitude in Northern and Central Europe: Decline, Resistance, and Expansion, edited by Paul Freedman and Monique Bourin, 131–78. Medieval Texts and Cultures of Northern Europe 9. Turnhout: Brepols, 2005.
Smalley, Beryl. The Study of the Bible in the Middle Ages. NDP 39. Notre Dame: University of Notre Dame Press, 1964.
Clanchy, M. T. Abelard: A Medieval Life. Oxford: Blackwell, 1997.