Our confocal microscope doesn't have a 350 laser -- the closest thing is 405. Is this at all possible? Are there any laser confocals with 350 lasers, or does it have to be done with a white light confocal?
I wouldn't be so sceptical, because from my experience from Leica TCS SP8, 405 nm is capable of exciting fluorophores such as DAPI or hoechst (whose spectra are almost identical to the Alexa350) with no problem and with very little power. If you would like to use shorter wavelengths, you would probably need to use UV optics which is not quite cheap. I don't have an experience with Alexa350 and I really can't promise you that it will work but I think it's definetely worth trying.
I think Alexa350 is mostly used in wide-field fluorescence microscopy where it can be imaged with a standard DAPI filterset. It's not often used in confocal microscopy because of the need for an appropriate UV laser. UV lasers are available but less commonly fitted to general purpose confocal microscopes.
We frequently use DAPI and Hoechst with 405nm lasers on our confocal microscopes but have not achieved satisfactory results with Alexa350.
I'm not sure what you mean by a "white light confocal" - but if you mean a 'white' laser such as the one offered by Leica this only covers the visible range and so would not be suitable for UV excitation.
Yes, it is kind of possible to do this. But why do it? It will be highly inefficient. Fluorophores can be excited to some extent over and beyond their peak excitation which is not a good way of exciting it. Besides, I have found that the Alexa 350 in particular is not a very good fluorophore to be used with most microscopes. The Planapo lenses mostly do not work with them as normal glass does not transmit in the deep UV range. You need planfluo lenses but even that most of the times do not give bright signal that you can easily get with the blue- and red-channels. The problem is compounded by the fact that most CCD cameras are not sensitive enough in the UV range. Bottom line is, try to avoid this 350 nm excitation.
My suggestion is that if you can use a good Alexa 488 or 568 dye with appropriate lasers. DAPI is a good dye in the UV range though, partly because its emission is very wide and can be detected easily with most detectors.