Does 17 January ever fall on Monday?

Yes it does. All dates fall on all days of the week, at some point or another. Taking just the 20th and 21st centuries, the 17th of January is on a Monday in the following years:

1910, 1916, 1921, 1927, 1938, 1944, 1949, 1955, 1966, 1972, 1977, 1983, 1994, 2000, 2005, 2011, 2022, 2028, 2033, 2039, 2050, 2056, 2061, 2067, 2078, 2084, 2089 and 2095.