Well no, not exactly.
In the first code of laws, in 1774: it simply said, with regard to umpires:
To allow 2 minutes for each man to come in when one is out, and 10 minutes between Each Hand to mark the Ball, that it may not be changed. They are sole judges of all outs and ins, of all fair and unfair Play, of frivolous delays, of all hurts, whether real or pretended, and are discretionally to allow whatever time they think Proper before the Game goes on again. In case of a real hurt to a striker, they are to allow another to come in, and the Person hurt to come in again, but are not to allow a fresh Man to Play on either side on any Account. They are sole judges of all hindrances, crossing the Players in running, and Standing unfair to Strike, and in case of hindrance may order a notch to be scored. They are not to order any man out unless appealed to by one of the Players. These Laws are to the Umpires Jointly. Each Umpire is the Sole Judge of all Nips and Catches, Ins and Outs, good or bad runs at his own Wicket, and his determination shall be absolute, and he shall not be changed for another Umpire without the Consent of both Sides. When the 4 Balls are bowled he is to call over. These Laws are seperately. When both Umpires shall call Play 3 Times, tis at the Peril of giving the Game from them that refuses Play.
Then by 1884, we have something rather interesting:
Law 51 No umpire shall be allowed to bet.
Law 52 No Umpire shall be changed during a match, unless with the consent of both sides, except in case of violation of Law 51; then either side may dismiss him.
It's not until the 2000 code, that there is mention of a replacement standing only at the striker's end.
So short answer, archie: No
