I wouldn't say the heart of Tornado Alley saw no tornadoes in May -- I know of a couple of people who personally saw tornadoes in Nebraska last month. SPC climo archives from last month show numerous days just in the first half of the month: 5/7 (12 tornado reports in Nebraska), 5/10 (19 tornado reports in Kansas, Nebraska, and W Iowa), 5/11 (about 12 reports in Kansas and Nebraska), 5/12 (13 reports in the Tx. Panhandle)...and numerous others.

May was, on the whole, below the 3 year average of tornado activity, but all other months besides February, which was at normal, were above average, if just barely so. The reasoning for why there was little tornado activity is sound, though...they just shouldn't make such a blanket statement about no tornadoes when the data shows otherwise.

As to your question: yes, it could, but only if the feature persisted for any length of time. The weather pattern in May was not very progressive, allowing such conditions to maintain themselves over a lengthy period of time. We already have some signs of that changing now, with an active week likely across the midwest. As soon as the blocking pattern over the eastern U.S. breaks down, probably in the next week, we'll see the overall weather pattern start to get back towards normal.