I don't believe so.
More interestingly, if the Lincoln game goes to a replay (which we win) and we are drawn at home in Round 5, we could have 6 (six) consecutive home games over 21 or 22 days:
7-8/2 - Lincoln
11/2 - Burton
14/2 - Ipswich
18/2 - FA Cup 5th Round
25/2 - Reading
28/2 - Newcastle...
I understand that the Football League nearly took this view when rescheduling the game was being batted around. The rule book says that 3 consecutive away games can only be played in exceptional circumstances.
We managed to win that one though...