yes, but it was only an issue in the sense that it allowed suspected christians to prove they were a 'good pious roman.' It was never required of the ordinary citizens en mass until Decius, so it is only really an issue to those denounced as christians. At this point one needs to consider far more the reasons why someone would be locally denounced.
the swearing of oaths to the emperor was something which many christians could do, and did. it really depends on what the oath in itself was, a simple oath to the emperor's genius under augustus should have posed no problems, as well into late antiquity christians still percieved a variety of intermediate figures between man and god, genius being one of the. cf. P.Brown- cult of saints Thus the oath would only be a problem if it was to the emperor's personal divinity, something which was never asserted during the Augustan period (in public/state religion anyway, although some private religious imagery does assert this link, eg Gemmae Augustae.
Also, the ability to swear an oath to the emperor was a way of avoiding the charges brought, just as demonstrating that your accuser was lying or it wasn't true for many other reasons. If one accepts the flagitia accusations as the basis for persecution then simply disprove the existance of flagitia and no oath would need to be taken. A.N. Sherwin-White is in part responsible for this idea of the oath and the rejection of imperial/magisterial power leading to persecutions, but i personally feel his theory based on the contumacia of the christians fails to account for the initial act of denouncement. After all, if the christians were not to be hunted out as Trajan replies to Pliny then why would they be infront of the provincial governor? it required an accusation, which can not be because they wouldn't swear the oath, because they were only asked once accused.
Interestingly, given the provincia assinged to Augustus in 27BC he might have avoided most of the ares where christian persecution generally occured, although it does crop up in most places at one point or another. It seems unlikely he would have excercised his maius imperium proconsularae to intervene in 'senatorial' provinces on this topic.