Ok, I've found the time to expand the solution I've figured out on 18 december and briefly mentioned in the comments.
The Problem
The <sj:datepicker timepicker="true"> tag correctly parses a Date object, but not its String representation. This is reported in Issue 1057, with status accepted but still not fixed.
This works:
<sj:datepicker displayFormat="dd/mm/yy" 
                  timepicker="true" 
                       value="%{new java.util.Date()}" />
This does NOT work:
<sj:datepicker displayFormat="dd/mm/yy" 
                  timepicker="true" 
                       value="%{'07/01/2015 14:42'}" />
When not using a Converter, you need to send the format of the date-time to a String variable, instead than to a Date one:
<sj:datepicker displayFormat="dd/mm/yy" 
                  timepicker="true" 
                        name="dateStr" />
private String dateStr; 
public void setDateStr(String dateStr){
    this.dateStr = dateStr;
}
public String getDateStr(){
    return dateStr;
}
If you need a Date (you probably do), you can use a String Getter and Setter, that will handle the parsing and the formatting between Date and String:
private static final String FORMAT = "dd/MM/yyyy HH:mm";
private Date date; 
public void setDateStr(String dateStr){
    date = new SimpleDateFormat(FORMAT,Locale.ITALIAN).parse(dateStr);
}
public String getDateStr(){
    return new SimpleDateFormat(FORMAT,Locale.ITALIAN).format(date);
}
But both this methods, due to the bug linked above, won't work. The solution is so easy that made me laugh in my last comment to the question:
The Solution
Use a String setter, and a Date getter, then it will work perfectly:
<sj:datepicker displayFormat="dd/mm/yy" 
                  timepicker="true" 
                        name="dateStr" 
                       value="date" />
private Date date; 
public void setDateStr(String dateStr){
    date = new SimpleDateFormat(FORMAT,Locale.ITALIAN).parse(dateStr);
}
public Date getDate(){
    return date;
}
(or write a Converter).
Side note: timepickerFormat="HH:mm" is not needed because HH:mm (24 hours format) is already the default format. You need to change it only if you want the 12 hours display format.