The ttk text entry widgets (e.g., ttk::entry, ttk::combobox) do not support the -insertOffTime option so it is not possible to stop cursor blink.
Using non-ttk widgets it is possible to stop cursor blink by putting *insertOffTime: 0 in the .Xdefaults file; but there doesn't appear to be any way to do this for the ttk widgets.
The problem appears in file generic/ttk/ttkBlink.c which has a TODO on this topic.
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I thought I'd add some rationale. First is that this functionality has been supported for years using insertOffTime for non-themed widgets. Second, even Microsoft finally recognized that some users cannot use software with blinking cursors and since Windows 2000 have provided a system-wide setting to switch off cursor blink. (And which the ttk widgets do not respect.) Apple have not been so considerate. For more about cursor blinking see for example: http://www.jurta.org/en/prog/noblink
I know that most people really like cursor blink since it helps them locate where they are. But a significant minority cannot work with blinking cursors. So I really hope you'll once more allow Tk to respect user preferences (just as you do for colors and fonts) with regard blinking.
The fact that it's got a TODO would be a fair indication that fixing this ought to be done. Don't know if it should be a style property or not...