Well if you go there, can one ever really aggregate risk exposures to different risk factors ? Not really, even something as simple as equity deltas can't really be aggregated, because there is no one realistic risk factor that when multiplied by such aggregate delta will give you your P&L.
What those measures do instead is give a broad understanding of the quantum of risk being run. They are only as good as the coherence of the individual factors they are summing up. In that sense an aggregate equity vega is relatively informative, because equity volatilities will tend to move together. If on top of that your portfolio is made up of similar equities (say similar market caps in the same sector), then our aggregate measure is likely to be quite informative.
Now, whether an aggregate vega over different asset classes is informative is up to the person who is aggregating them. I guess the important thing here is whether this is meant to be a precise reflection of risk run (it isn't), or a broad indication meant to help compare the portfolio at different points in time, for example (it probably is ok for that).