No, an invasive species is one that is an alien to the area and that is likely to cause damage to the ecosystem it is now present in. [1] Human influence is the main cause, but species may get there by other means. [2] Transport vector is unimportant to the definition of invasive species or not. One study considers a definition where species which are native but that are causing ecological damage could be considered an 'invasive species'. [3]

Also from [3]:

> Invading propagules begin as residents in a potential donor region (stage 0), some of which are taken into the transport vector (stage I), usually by humans. If these propagules survive transport and release to become introduced (stage II), they have the potential to establish (stage III) in a novel environment.

Note that 'stage I' notes 'usually by humans', not 'by humans'. Ie. a species which uses some natural phenomena as a transport vector can still be considered an invasive species. [1] says similar - "Human actions are the primary means of invasive species introductions." - implying that non-human methods are also possible for invasive species introductions.

It's nonsensical to say that as soon as something migrates using a natural phenomena that it becomes a 'native' to that area.

[1] https://www.invasivespeciesinfo.gov/whatis.shtml [2] https://www.invasivespeciesinfo.gov/toolkit/vectors.shtml [3] http://www.esf.edu/efb/parry/502_reading/colautti2004.pdf