No, the "Alignment" has nothing to do with "silkscreen" showing up as "copper", etc. Altium has built-in standards to make sure that the layers, etc are identified correctly in all cases.
I expect the "Alignment" has to do primarily with Altium versions (i.e. someone might run Altium 14 and someone else might run Altium 16). There are differences between 14 and 16 (i.e. multiline silkscreen text entry is supported in 16 but not 14), and if multiline text entry is used in 16 and the file is opened in 14, the text shows up on one line with very long spaces where the line breaks should be. That is the only issue I have seen (there are quite a few Altium users where I work), so it's important that everyone has the same version of Altium. Silkscreen will never show up as copper unless someone physically makes that change (puts the text on another layer). Perhaps other "alignment" aspects would be design rules, template files, libraries, etc. That's all common sense though, and would be applicable to any package (Eagle included). It shouldn't be difficult to keep everyone on the same page when using Altium -- It does a lot of the work for you in the background and is very consistent. Everything is hard-coded.
The only semi-difficult "alignment" issue might be layer colors (each user has the ability to change his own layer colors) but I have never found that to be an issue. For example, one user may use red for the top layer and blue for the bottom layer, while another user might use yellow for the top layer and green for the bottom layer (this doesn't happen often, if ever, where I work, but it CAN happen). However, all of the layers are clearly labeled ("Top Layer", "Signal Layer 1", "Signal Layer 2", "Bottom Layer", etc) so this shouldn't be a problem.