By definition, a grandfather clause meant that (white) people could bypass poll taxes, literacy tests, and other barriers if their grandfathers had been previously eligible to vote, as African Americans could not ever qualify. These were put in place to specifically deny African Americans the right to vote.

Even if a white person didn't qualify under the grandfather clause, voter registrars would ask different, impossible to answer questions to black people (such as "recite the entire constitution" or more bizarrely "how many bubbles are there in a bar of soap") than the easier questions to whites.

The source below gives a good overview, I would also recommend Taylor Branch's books on the civil rights movement.

http://www.blackpast.org/aah/grandfather-clause-1898-1915

Basically, those mechanisms were put in place specifically to deny the vote to African Americans and it was up to local registrars to enforce it and to make sure whites were able to vote. It's possible some potential white voters were swept up in all that, but I've never heard of that happening.

Voting tests were enforced in a heavily discriminatory manner. For example, some states had understanding clauses, which asked voters to explain a portion of the constitution to see if they properly understood it. Here is a federal court explaining how the test was administered in Louisiana (emphasis mine):

As in the selection process, gross abuses of discretion appear in the evaluation of the interpretations. One rejected Negro applicant stated that the registrar ‘said what I was saying was right, but it wasn't like she wanted me to say it’.

Most of the interpretation tests have been administered orally, thus precluding the use of written records as a check on what the registrar accepted as reasonable interpretations. Nevertheless, the record shows that interpretations far less responsive to the constitutional text selected have been accepted from whites than from Negroes. Compounding this with the fact that Negroes were often given more difficult sections to interpret, the bias in favor of the whites becomes readily apparent.

Some parishes administered written examinations and kept records of the questions asked and the responses accepted. In these examinations the registrar usually employed one or more of several sets of cards containing selected sections of the Constitution and a space for the applicant's interpretation of it. Even the most cursory glance at the records in these parishes underscores the heavy burden under which Negro applicants were laboring. In one set of cards, there is great disparity in the difficulty of the questions asked. This enables the registrar to select cards with simple sections for white applicants and difficult cards for Negroes. There is unmistakable evidence that many white applicants were shown cards with sample answers on them. Some applicants admitted this, and there is even an instance of a white applicant having, by mistake, signed the sample answer card. Negroes were not allowed to see the acceptable answers, let alone copy them. Similarly, the pattern of the answers indicates that the registrars often told white applicants the currently acceptable answers. The phraseology of almost every answer in one parish changed right along with the registrar's change in the wording of the acceptable answer.

Registrars were easily satisfied with answers from white voters. In one instance ‘FRDUM FOOF SPETGH’ was an acceptable response to the request to interpret Article 1, § 3 of the Louisiana Constitution.

On the other hand, the record shows that Negroes whose application forms and answers indicate that they are highly qualified by literacy standards and have a high degree of intelligence have been turned down although they had given a reasonable interpretation of fairly technical clauses of the constitution. For example the Louisiana Constitution, Article X, § 16 provides: ‘Rolling stock operated in this State, the owners of which have no domicile therein, shall be assessed by the Louisiana Tax Commission, and shall be taxed for State purposes only, at a rate not to exceed forty mills on the dollar assessed value.’ The rejected interpretation was: ‘My understanding is that it means if the owner of which does not have residence within the State, his rolling stock shall be taxed not to exceed forty mills on the dollar.’

In another instance the registrar rejected the following interpretation of the Search and Seizure provision of the Fourth Amendment: ‘(N)obody can just go into a person's house and take their belongings without a warrant from the law, and it had to specify in this warrant what they were to search and seize.’ Another rejected interpretation of the same Amendment by a Negro applicant was: ‘To search you would have to get an authorized authority to read a warrant.’ The Louisiana Constitution Article I, § 5 provides: ‘The people have the right peaceably to assemble.’ A registrar rejected the following interpretation: ‘That one may assemble or belong to any group, club, or organization he chooses as long as it is within the law.’

http://law.justia.com/cases/federal/district-courts/FSupp/225/353/1872222/

Voter turnout, even among whites, was far lower in the South than elsewhere in the country, and the culprit was the poll tax. You might be interested in this 1940 article by George C. Stoney, who was doing research for Gunnar Myrdal at the time.

He quotes a political observer from San Antonio, who explained how the tax acted as a disincentive for voters and a source of corruption:

Haying a poll tax in February to vote in November is to most folks in Texas like buying a ticket to a show nine months ahead of time, and before you know who's playing or really what the thing is all about. It is easy to forget to do, too, and here is where the politicians are obliging. They buy up as many poll tax receipts as they can before the books close, keep them on file and pass them out to their owners' on election day—with instructions, of course, and an extra dollar or so for sweetenin'. There is a law about no person being allowed to pay anybody else's poll tax; but that, like the one about people who don't pay being given road work or a fine, is enforced only when it's convenient.

Stoney listed the voter turnout for the Democratic primary in various poll-tax states - remember that since the South was a one-party region, the primary was effectively the main election - and found turnout ranging from 14.1% in South Carolina to 33.5% for Tennessee. The turnout was generally markedly higher in non-poll tax Southern states.

It's hard to determine exactly how much this low turnout was due to the poll tax, but there certainly was a correlation. J. Morgan Kousser, in The Shaping of Southern Politics: Suffrage Restriction and the Establishment of the One-Party South, 1880–1910 (pp. 67-68) estimated that the poll tax in Georgia may have reduced overall voter turnout by 16% to 28%, and black turnout by half.