It depends what you mean big lots.
1-10 lots are quite big trades and they don't usually affect the price (in most brokers that is), but if you open a 20-100 lots trade then you will probably see a delay and a quite different price, than opening a small trade at the same exact time.
So you mean, 1 -10 lots size in each trade won't affect the future price. My point of saying this is that If you do big lots. others thinks that they might like to lose your trade inorder that the will win.
I spoke with some broker that it's true if you win, others will lose the trade within the broker's client and if I traded big lots, and the opposite side doesn't have much money to trade with. then the intra bank will be on my opposite side of trade. Which means I'm betting against the bank. If so, then I'm thinking if the bank would twist or tweak the trade inorder for them to win. Will this make this logic sense to you?
You are in deep waters now.
Only a few people could give you a solid answer on this argument.
I don't think that there is yes/no answer to that.
It depends on the broker, pair traded, time of the day, period of the year, the news involved, how many pro traders and banks are active at the monent, your trading decision and many more other reasons.
There isn't a yes/no answer to your question.
No conrete answers on this.
Most of the time, yes.