Yes, to the extent permitted by the regulatory system of the time, which remained in effect until the Staggers Act of 1980, and the regulators' view was that trucking was a fledgling industry in need of protection from the predatory railroads. An important regulatory principle at the time was that freight charges on a shipment should be kept low in proportion to the intrinsic value of the commodity; this meant that low-value commodities had low rates, even if below cost, while high-value commodities could have rates comfortably in excess of costs while still remaining low compared to value. This seemed to work well as long as everything moved by rail, since what the railroads lost on handling low-rated freight was made up for by the high-rated freight. With the advent of the internal-combustion engine, the pneumatic tire (the first ones were solid rubber), and a network of paved highways, trucking over long distances became practical and the truckers, not having been born yesterday, could easily offer reduced rates on high-value commodities while leaving the low-rated stuff to the railroads. The railroads were left with the choice of reducing rates on high-value commodities and having less left over to pay for the low-rated traffic, or not reducing them and losing all the revenue. It was almost a lose-lose situation whatever they did as long as truckers weren't--and still aren't--required to haul the sand, gravel, and broken glass (there were freight rates on broken glass before the word recycling entered the language).
In 1935, interstate trucking was brought under regulation by legislation made a part of the existing Act to Regulate Commerce; the Interstate Commerce Commission, created in 1887, being charged with regulating the industry. The main concern was to prevent having too many trucks chasing too little business, so the right of truckers to haul freight had to be sought from and granted by the ICC*, truckers being forbidden to haul anything between any points without specific authority from the ICC. Thus, if there was any low-rated traffic a trucker didn't want to handle he simply didn't apply for authority to carry it, which meant he was legally prohibited from doing so.
Under the 1935 legislation, carriage of agricultural products was exempt from regulation when moving by truck but not when moving by rail since there was no intent to regulate traffic moving from farm to railhead. However, that intent was not incorporated into the language of the Act, with the result that, among other things, frozen French fries shipped from Idaho to New York were exempt from rate regulation when moving by truck, but not when moving by rail. Under the law it took at least 30 days for a railroad to change a freight rate, and only then if there were no objections--it could take up to 9 months and more if challenged before the ICC. (And it was not necessary for a party to have "standing" to initiate a protest; anybody could object.) It was not until the Staggers Act and the Motor Carrier Act, both of 1980, that both truck and rail transportation was largely freed from the conditions of the 1920's and -30's.
* The seeking and granting of motor-carrier operating rights became a whole subset of law practice after 1935.