As you might expect, there has been some debate over the years over exactly who "God-fearers" were.  Nevertheless, we have every reason to accept the basic picture of Acts, where many of the earliest Gentile converts to the Jesus movement were already sympathetic to Judaism and had frequented the synagogue (e.g., Acts 10:2, 22, 35; 13:16, 26, 43, 50; 16:14; 17:4, 17; 18:7).  While Philo and Josephus may exaggerate their accounts, their depictions of the attractiveness of Jewish law and custom ring true with what evidence we have.  Even Roman historians make passing comments that indicate substantial interest in Judaism by Romans, including some elites.  Augustine quotes Seneca, referencing sympathizers to Judaism, complaining about how "the conquered have given their laws to the victors."  The Roman satirist Juvenal similarly mocked those who go beyond their parents, who merely followed some Jewish customs. Their children, he complains, go on to become circumcised and fully converted. 
This last reference is significant, because it points to a readiness on the part of many to convert fully to Judaism. That is to say, it verifies the picture in Galatians of Gentile believers who would consider circumcision. If there was significant enough interest in Judaism to draw such frequent criticism by Roman elites like Juvenal, Tacitus, and Seneca--and in relation to conversion in general--then we can easily see that Gentile converts to the Jesus movement might be susceptible to such pressure. Indeed, they would likely be more susceptible, given the apocalyptic pressure of Jesus' imminent return...
 For those who have most leaned away from the majority position, see Alfred Bertholet, Die Stellung der Israeliten und der Juden zu den Fremden (Leipzig: Mohr, 1896); Kirsopp Lake, "Proselytes and God fearers," in The Acts of the Apostles, F. F. Jackson and K. Lake, eds. (London: Macmillan, 1933), 74-96; Max Wilcox, "The God fearers in Acts--A Reconsideration," JSNT 13 (1981): 102-22; Louis H. Feldman (more balanced), Jew and Gentile in the Ancient World (Princeton: Princeton University, 1993), 342-82; Judith Lieu, "The Synagogue and Separation of the Christians," The Ancient Synagogue from its Origins until 200C.E. (Stockholm: Almqvist & Wiksell, 2003), 189-207.
 Cf. James D. G. Dunn, Beginning with Jerusalem (Grand Rapids: Eerdmans, 2008), 297-99, 560-63.
 E.g., Philo, Mos. 2.17-24; Josephus, War 7.45; Ant. 14:110; Ap. 1.166-67; 2.282.
 E.g., Suetonius, Tiberius 36; Domitian 12.2; Dio Cassius, Roman History 67.14.1-2; Petronius, fr. 37; Epictetus, quoted in Arrian, Dissertationes 2.19-21.
 In City of God 6.11.
 Satires 14.96-99.