Just adding to what IstvanPetrie and Chris said; there really should be a 'rule' about when and how you should alternate pick or pick in any other way. You're making sound and it should sound good. However you get there with picking, do it.

Keeping that in mind, adding to Chris, different stroke directions have a different timbers and can matter on how the solo sounds. Even in rhythms, you can tell. I was listening to the Aerosmith's song 'Toys in the Attic' and noticing, even after having played it in the past, that the rhythm is not a consistent up or down pattern. I mean, it follows a pattern in terms of 'up-down-down-up-down' strumming but the same chord could be upstroked or downstroked. It's what makes the riff cool. I know, not a solo example but an example nontheless.

To be honest, I've never much thought about 'how; I did it. I just played how it felt. If you buy in to too much 'I must play with this technique', you're gonna miss some cool stuff. In the 80's, I heard sooo many times that 'you must alternate pick everything'. I loved alternate picked shredding. I did it a lot. Just didn't care if I was 'true' to the technique. Only that what I did sounded good.....cuz that's the point.

So, when you're soloing stuff. Play with it a bit. Have fun with playing with it. You're gonna crash-n-burn. But fun while doing it and you'll find out about how it all works.