Very unlikely. Records do indicate that Richard was on travel when Edward IV was conceived, but there's no reason to think Cecily didn't travel with Richard. They were very close and she had accompanied him before.

In all likelihood, rumors were spread about his illegitimacy by his brother George, and his cousin Richard Earl of Warwick. When Edward married Elizabeth Woodville, it ruined Richard's chances of controlling Edward. So, he plotted with George to make George king, and spread rumors about Edward's paternity.

Source: Alison Weir's Elizabeth of York.

There is certainly some conjecture that Edward was illegitimate, especially as Richard was away from Rouen (where Edward was born) for an extended period. Cecily is accused by some historians (and some contemporaries) of having an affair with an archer called Blaybourne. Contemporary rumour of such an affair would certainly have been exasperated by those who could gin from Edward's downfall (namely George, duke of Clarence and the earl of Warwick). However, it is also unlikely that such an accusation will have appeared from nowhere. The argument that Edward could not have been illegitimate:

• it would have been very difficult for Cecily to engage in such a dalliance without supporters/friends of the duke of York finding out.
• when a baby is born is not an exact science, and Edward could have been born either early or late, blurring the reliability of the timelines a little. -Pontoise (where Richard was) was actually only about 80 miles from Rouen, not 'over a hundred' as has been claimed. The argument that Edward was illegitimate:
• Edward's comparatively simple baptism was in stark contrast to that of his brother Edmund's extravagant baptism only around a year later. Although, of course the quality of a baptism is by no means definitive proof to the legitimacy of Edward.
• Edward was tall and fair, his father (?) was short and dark haired, the lack of family resemblance also contributes to the debate. However, not many of the York children resembled their parents and no one seems to be questioning their legitimacy.
• Cecily, his mother, reportedly, upon hearing of Edward's unpopular marriage to Elizabeth Woodville, exclaimed that Edward was illegitimate. Although, how much of this was a last ditch attempt to get him to go through with the marriage proposal arranged by Warwick, and how much was truth, cannot be known. Of course, as much as this is an interesting topic to debate, the fact that York recognised Edward as his son and heir technically legitimises him, at least in the sense of inheriting the throne. Richard would never have publicly claimed that Edward was illegitimate, and Cecily's claim can hardly be considered conclusive proof.Also, those who spread the rumour had too many motives and reasons for wanting Edward off the throne for their claims to be taken too seriously. However, the possibility that Edward was illegitimate will never, and can never, be entirely eradicated.