It can make a big difference. BTDT more than once when I was on the road and had to buy whatever tires a small town tire dealer had in stock.
Bias ply on the trailer can create problems with tracking the tow vehicle.....
and much depends on the tread type and pattern.
The old rib type bias ply truck tires on a trailer tracked the tow vehicle with radials much better then the usual ST tire tread pattern that looks like a AT type tire tread (Marathons/Maxxis 8008/several other ST tire brands).
If you have bias on the trailer go ahead and run them but be aware if the combo has handling issues.
"good judgment comes from experience, and a lot of that comes from bad judgment" ............ Will Rogers
'03 2500 QC Dodge/Cummins HO 3.73 6 speed manual Jacobs Westach
'97 Park Avanue 28' 5er 11200 two slides